Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice
Institute of Scientific and Technical Information of China (English)
XU; Quan; TIAN; Qiang
2005-01-01
The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2D) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.
Gap solitons in periodic Schrodinger lattice system with nonlinear hopping
Directory of Open Access Journals (Sweden)
Ming Cheng
2016-10-01
Full Text Available This article concerns the periodic discrete Schrodinger equation with nonlinear hopping on the infinite integer lattice. We obtain the existence of gap solitons by the linking theorem and concentration compactness method together with a periodic approximation technique. In addition, the behavior of such solutions is studied as $\\alpha\\to 0$. Notice that the nonlinear hopping can be sign changing.
Dirac-Point Solitons in Nonlinear Optical Lattices
Xie, Kang; Boardman, Allan D; Guo, Qi; Shi, Zhiwei; Jiang, Haiming; Hu, Zhijia; Zhang, Wei; Mao, Qiuping; Hu, Lei; Yang, Tianyu; Wen, Fei; Wang, Erlei
2015-01-01
The discovery of a new type of solitons occuring in periodic systems without photonic bandgaps is reported. Solitons are nonlinear self-trapped wave packets. They have been extensively studied in many branches of physics. Solitons in periodic systems, which have become the mainstream of soliton research in the past decade, are localized states supported by photonic bandgaps. In this Letter, we report the discovery of a new type of solitons located at the Dirac point beyond photonic bandgaps. The Dirac point is a conical singularity of a photonic band structure where wave motion obeys the famous Dirac equation. These new solitons are sustained by the Dirac point rather than photonic bandgaps, thus provides a sort of advance in conceptual understanding over the traditional gap solitons. Apart from their theoretical impact within soliton theory, they have many potential uses because such solitons have dramatic stability characteristics and are possible in both Kerr material and photorefractive crystals that poss...
Institute of Scientific and Technical Information of China (English)
LI De-Jun; MI Xian-Wu; DENG Ke; TANG Yi
2006-01-01
In the classical lattice theory, solitons and locaLized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solitons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j = j0.
Asymmetric soliton mobility in competing linear-nonlinear PT-symmetric lattices
Kartashov, Yaroslav V; Torner, Lluis
2016-01-01
We address the transverse mobility of spatial solitons in competing parity-time-symmetric linear and nonlinear lattices. The competition between out-of-phase linear and nonlinear lattices results in a drastic mobility enhancement within a range of soliton energies. We show that within such range, the addition of even a small imaginary part in the linear potential makes soliton mobility strongly asymmetric. The minimal phase tilt required for setting solitons into radiationless motion across the lattice in the direction opposite to that of the internal current drops to nearly zero, while the minimal phase tilt required for motion in the opposite direction notably increases. For a given initial phase tilt, the velocity of soliton motion grows with an increase of the balanced gain/losses. In this regime of enhanced mobility, tilted solitons can efficiently drag other solitons that were initially at rest, to form moving soliton pairs.
Lattice solitons in nonlinear Schrödinger equation with coupling-to-a-mean-term
Bağcı, Mahmut; Bakırtaş, İlkay; Antar, Nalan
2017-01-01
Wave collapse is arrested in the self-focusing nonlinear Schrödinger equation with coupling to a mean term (NLSM) by adding an external potential (lattice) to the governing equation. It is numerically demonstrated that collapse will eventually occur in a lattice-free system and it can be suppressed by adding an external periodic lattice to the governing system. It is numerically shown that lattice depth provides great controllability on soliton stability and more robust solitons can be obtained.
Orientation-dependent excitations of lattice soliton trains with hybrid nonlinearity.
Hu, Yi; Lou, Cibo; Liu, Sheng; Zhang, Peng; Zhao, Jianlin; Xu, Jingjun; Chen, Zhigang
2009-04-01
We demonstrate selective excitation of soliton trains residing in different gaps or within the same Bloch band of a new type of photonic lattice merely by changing the orientation of an input probe beam. A self-focusing and -defocusing hybrid nonlinearity as established in a nonconventionally biased photorefractive crystal leads to controlled soliton transitions from different band edges or subband edges, in good agreement with our theoretical analysis.
Weakly deformed soliton lattices
Energy Technology Data Exchange (ETDEWEB)
Dubrovin, B. (Moskovskij Gosudarstvennyj Univ., Moscow (USSR). Dept. of Mechanics and Mathematics)
1990-12-01
In this lecture the author discusses periodic and quasiperiodic solutions of nonlinear evolution equations of phi{sub t}=K (phi, phi{sub x},..., phi{sup (n)}), the so-called soliton lattices. After introducing the theory of integrable systems of hydrodynamic type he discusses their Hamiltonian formalism, i.e. the theory of Poisson brackets of hydrodynamic type. Then he describes the application of algebraic geometry to the effective integration of such equations. (HSI).
Vector Lattice Vortex Solitons
Institute of Scientific and Technical Information of China (English)
WANG Jian-Dong; YE Fang-Wei; DONG Liang-Wei; LI Yong-Ping
2005-01-01
@@ Two-dimensional vector vortex solitons in harmonic optical lattices are investigated. The stability properties of such solitons are closely connected to the lattice depth Vo. For small Vo, vector vortex solitons with the total zero-angular momentum are more stable than those with the total nonzero-angular momentum, while for large Vo, this case is inversed. If Vo is large enough, both the types of such solitons are stable.
Subwavelength vortical plasmonic lattice solitons.
Ye, Fangwei; Mihalache, Dumitru; Hu, Bambi; Panoiu, Nicolae C
2011-04-01
We present a theoretical study of vortical plasmonic lattice solitons, which form in two-dimensional arrays of metallic nanowires embedded into nonlinear media with both focusing and defocusing Kerr nonlinearities. Their existence, stability, and subwavelength spatial confinement are investigated in detail.
Dark Solitons in FPU Lattice Chain
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton.Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.
Surface solitons in trilete lattices
Stojanovic, M; Hadzievski, Lj; Malomed, B A
2011-01-01
Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schr\\"{o}dinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter -- actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, ...
The 3D solitons and vortices in 3D discrete monatomic lattices with cubic and quartic nonlinearity
Institute of Scientific and Technical Information of China (English)
Xu Quan; Tian Qiang
2006-01-01
By virtue of the method of multiple-scale and the quasi-discreteness approach, we have discussed the nonlinear vibration equation of a 3D discrete monatomic lattice with its nearest-neighbours interaction. The 3D simple cubic lattices have the same localized modes as a ID discrete monatomic chain with cubic and quartic nonlinearity. The nonlinear vibration in the 3D simple cubic lattice has 3D distorted solitons and 3D envelop solitons in the direction of kx = ky = kz = k and k =±π/6a0 in the Brillouin zone, as well as has 3D vortices in the direction of kx = ky = kz = k and k =±π/a0 in the Brillouin zone.
Zeng, Jianhua
2013-01-01
It is commonly known that stable bright solitons in periodic potentials, which represent gratings in photonics/plasmonics, or optical lattices in quantum gases, exist either in the spectral semi-infinite gap (SIG) or in finite bandgaps. Using numerical methods, we demonstrate that, under the action of the cubic self-focusing nonlinearity, defects in the form of "holes" in two-dimensional (2D) lattices support continuous families of 2D solitons \\textit{embedded} into the first two Bloch bands of the respective linear spectrum, where solitons normally do not exist. The two families of the \\textit{embedded defect solitons} (EDSs) are found to be continuously linked by the branch of \\textit{gap defect solitons} (GDSs) populating the first finite bandgap. Further, the EDS branch traversing the first band links the GDS family with the branch of regular defect-supported solitons populating the SIG. Thus, we construct a continuous chain of regular, embedded, and gap-mode solitons ("superfamily") threading the entire ...
Unstaggered-staggered solitons in two-component discrete nonlinear Schr\\"{o}dinger lattices
Malomed, Boris A; Van Gorder, Robert A
2012-01-01
We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schr\\"{o}dinger (DNLS) equations with the attractive self-phase-modulation (SPM) nonlinearity, coupled by the repulsive cross-phase-modulation (XPM) interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite accurately, and are stable. Close to a boundary of the existence region of the solitons (which may feature several connected branches), there are broad solitons which are not well approximated by the VA, and are unstable.
Matter-wave bright solitons in effective bichromatic lattice potentials
Indian Academy of Sciences (India)
Golam Ali Sekh
2013-08-01
Matter-wave bright solitons in bichromatic lattice potentials are considered and their dynamics for different lattice environments are studied. Bichromatic potentials are created from superpositions of (i) two linear optical lattices and (ii) a linear and a nonlinear optical lattice. Effective potentials are found for the solitons in both bichromatic lattices and a comparative study is done on the dynamics of solitons with respect to the effective potentials. The effects of dispersion on solitons in bichromatic lattices are studied and it is found that the dispersive spreading can be minimized by appropriate combinations of lattice and interaction parameters. Stability of nondispersive matter-wave solitons is checked from phase portrait analysis.
Solitons in spiraling Vogel lattices
Kartashov, Yaroslav V; Torner, Lluis
2012-01-01
We address light propagation in Vogel optical lattices and show that such lattices support a variety of stable soliton solutions in both self-focusing and self-defocusing media, whose propagation constants belong to domains resembling gaps in the spectrum of a truly periodic lattice. The azimuthally-rich structure of Vogel lattices allows generation of spiraling soliton motion.
Spatial solitons in photonic lattices with large-scale defects
Institute of Scientific and Technical Information of China (English)
Yang Xiao-Yu; Zheng Jiang-Bo; Dong Liang-Wei
2011-01-01
We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.
Two-dimensional subwavelength plasmonic lattice solitons
Ye, F; Hu, B; Panoiu, N C
2010-01-01
We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detai
Interaction of discrete nonlinear Schr\\"odinger solitons with a linear lattice impurity
Brazhnyi, Valeriy A; Rodrigues, A S
2013-01-01
The interaction of moving discrete solitons with a linear Gaussian defect is investigated. Solitons with profiles varying from hyperbolic secant to exponentially localized are considered such that the mobility of soliton is maintained; the condition for which is obtained. Studies on scattering of the soliton by an attractive defect potential reveal the existence of total reflection and transmission windows which become very narrow with increasing initial soliton amplitude. Transmission regions disappear beyond the small-amplitude limit. The regions of complete reflection and partial capture correspond to the windows of the existence and nonexistence of solution of the stationary problem. Interaction of the discrete soliton with a barrier potential is also investigated. The critical amplitude of the defect at which splitting of the soliton into two parts occurs was estimated from a balance equation. The results were confirmed through direct numerical integration of the dynamical equation showing very good agre...
Stability analysis for solitons in PT-symmetric optical lattices
Nixon, Sean; Yang, Jianke
2012-01-01
Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase-transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while stable families of solitons can exist in PT lattices, increasing the gain-loss component has an overall destabilizing effect on soliton propagation. Specifically, when the gain-loss component increases, the parameter range of stable solitons shrinks as new regions of instability appear. Thirdly, we investigate the nonlinear evolution of unstable PT solitons under perturbations, and show that the energy of perturbed solitons can grow unbounded even though the PT lattice is below the phase transition point.
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Lin Xiao-Gang; Liu Wen-Jun; Lei Ming
2016-03-01
Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota’s bilinear method. The bilinear forms and analytic soliton solutions are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.
Optical lattice trap for Kerr solitons
Taheri, Hossein; Matsko, Andrey B.; Maleki, Lute
2017-06-01
We show theoretically and numerically that dichromatic pumping of a nonlinear microresonator by two continuous wave coherent optical pumps creates an optical lattice trap that results in the localization of intra-cavity Kerr solitons with soliton positions defined by the beat frequency of the two pumps. This phenomenon corresponds to the stabilization of the comb repetition rate. The locking of the second pump, through adiabatic tuning of its frequency, to the comb generated by the first pump allows transitioning to single-soliton states, manipulating the position of Kerr solitons in the cavity, and tuning the frequency comb repetition rate within the locking range. It also explains soliton crystal formation in resonators supporting a dispersive wave emitted as a result of higher-order group velocity dispersion or avoided mode crossing. We show that dichromatic pumping by externally stabilized pumps can be utilized for stabilization of microresonator-based optical frequency combs when the comb span does not cover an octave or a significant fraction thereof and standard self-referencing techniques cannot be employed. Our findings have significant ramifications for high-precision applications of optical frequency combs in spectrally pure signal generation, metrology, and timekeeping.
Beam evolutions of solitons in strongly nonlocal media with fading optical lattices
Institute of Scientific and Technical Information of China (English)
Dai Zhi-Ping; Lu Shi-Zhuan; You Kai-Ming
2013-01-01
We address the impact of imprinted fading optical lattices on the beam evolution of solitons in strongly nonlocal nonlinear media.The results show that the width of the soliton experiences a change with the increasing propagation distance,the critical power for the soliton varies with the lattice fading away,and the soliton breathing is affected by the initial lattice depth and the nonlocality degree.
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton p...
Spatial solitons in nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....
Naether, Uta; Johansson, Magnus
2010-01-01
We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schr\\"odinger model with saturable on-site nonlinearity. A numerical constrained Newton-Raphson method is used to calculate two-dimensional Peierls-Nabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phase-space trajectories passing close to stationary modes. Investigating the two-parameter space of the model through independent variations of the nonlinearity constant and the power, we show how parameter regimes and directions of good mobility are connected to existence of smooth surfaces connecting the stationary states. In particular, directions where solutions can move with minimum radiation can be predicted from flatter parts of the surfaces. For such mobile solutions, slight perturbations in the transverse direction yield additional transverse oscillations w...
Knotted solitons in nonlinear magnetic metamaterials.
Rosanov, Nikolay N; Vysotina, Nina V; Shatsev, Anatoly N; Desyatnikov, Anton S; Kivshar, Yuri S
2012-03-30
We demonstrate that nonlinear magnetic metamaterials comprised of a lattice of weakly coupled split-ring resonators driven by an external electromagnetic field may support entirely new classes of spatially localized modes--knotted solitons, which are stable self-localized dissipative structures in the form of closed knotted chains. We demonstrate different topological types of stable knots for the subcritical coupling between resonators and instability-induced breaking of the chains for the supercritical coupling.
Discrete flat-band solitons in the Kagome lattice
Vicencio, Rodrigo A
2013-01-01
We consider a model for a two-dimensional Kagome-lattice with defocusing nonlinearity, and show that families of localized discrete solitons may bifurcate from localized linear modes of the flat band with zero power threshold. Such fundamental nonlinear modes exist for arbitrarily strong nonlinearity, and correspond to unique configurations in the limit of zero inter-site coupling. We analyze their linear stability, and show that by choosing dynamical perturbations close to soft internal modes, a switching between solitons of different families may be obtained. In a window of small values of norm, a symmetry-broken localized state is found as the lowest-energy state.
Solitons of a vector model on the honeycomb lattice
Vekslerchik, V. E.
2016-11-01
We study a simple nonlinear vector model defined on the honeycomb lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the Hirota bilinear difference equation and the Ablowitz-Ladik system. This result is used to derive the N-soliton solutions.
Nonlinear dynamics of soliton gas with application to "freak waves"
Shurgalina, Ekaterina
2017-04-01
So-called "integrable soliton turbulence" attracts much attention of scientific community nowadays. We study features of soliton interactions in the following integrable systems: Korteweg - de Vries equation (KdV), modified Korteweg - de Vries equation (mKdV) and Gardner equations. The polarity of interacted solitons dramatically influences on the process of soliton interaction. Thus if solitons have the same polarity the maximum of the wave field decreases during the process of nonlinear interactions as well statistical moments (skewness and kurtosis). In this case there is no abnormally large wave formation and this scenario is possible for all considered equation. Completely different results can be obtained for a soliton gas consisted of solitons with different polarities: such interactions lead to an increase of resulting impulse and kurtosis. Tails of distribution functions can grow significantly. Abnormally large waves (freak waves) appear in such solitonic fields. Such situations are possible just in case of mKdV and Gardner equations which admit the existence of bipolar solitons. New effect of changing a defect's moving direction in soliton lattices and soliton gas is found in the present study. Manifestation of this effect is possible as the result of negative phase shift of small soliton in the moment of nonlinear interaction with large solitons. It is shown that the effect of negative velocity is the same for KdV and mKdV equations and it can be found from the kinematic assumption without applying the kinetic theory. Averaged dynamics of the "smallest" soliton (defect) in a soliton gas, consisting of solitons with random amplitudes is investigated. The averaged criterion of velocity sign change confirmed by numerical simulation is obtained.
Three-dimensional topological solitons in PT-symmetric optical lattices
Kartashov, Yaroslav V; Huang, Guoxiang; Torner, Lluis
2016-01-01
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying soliton states. The imaginary part of the lattice induces internal currents in the solitons that strongly affect their domains of existence and stability. The domain of stability for fundamental solitons can extend nearly up to the PT-symmetry breaking point, where the linear lattice spectrum becomes complex. Vortex solitons feature spatially asymmetric profiles in the PT-symmetric lattices, but they are found to still exist as stable states within narrow regions. Our results provide the first example of continuous families of stable three-dimensional propagating solitons supported by complex potentials.
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
2016-09-01
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain.
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families...
Energy Technology Data Exchange (ETDEWEB)
Lebedev, M. E., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Alfimov, G. L., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com [National Research University of Electronic Technology MIET, Zelenograd, Moscow 124498 (Russian Federation); Malomed, Boris A., E-mail: malomed@post.tau.ac.il [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Laboratory of Nonlinear-Optical Informatics, ITMO University, St. Petersburg 197101 (Russian Federation)
2016-07-15
We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.
Nonlinear compression of optical solitons
Indian Academy of Sciences (India)
M N Vinoj; V C Kuriakose
2001-11-01
In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single ﬁeld in a ﬁber medium with phase modulation and ﬁbre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modiﬁed NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects.
Spatiotemporal dissipative solitons in two-dimensional photonic lattices.
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2008-11-01
We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the truncated two-dimensional photonic lattice. We find the domains of existence and stability of such spatiotemporal dissipative solitons in the relevant parameter space, for both on-site and intersite lattice solitons. We show that the on-site solitons are stable in the whole domain of their existence, whereas most of the intersite solitons are unstable. We describe the scenarios of the instability-induced dynamics of dissipative solitons in two-dimensional lattices.
Soliton form factors from lattice simulations
Rajantie, Arttu
2010-01-01
The form factor provides a convenient way to describe properties of topological solitons in the full quantum theory, when semiclassical concepts are not applicable. It is demonstrated that the form factor can be calculated numerically using lattice Monte Carlo simulations. The approach is very general and can be applied to essentially any type of soliton. The technique is illustrated by calculating the kink form factor near the critical point in 1+1-dimensional scalar field theory. As expected from universality arguments, the result agrees with the exactly calculable scaling form factor of the two-dimensional Ising model.
Deceleration of the small solitons in the soliton lattice: KdV-type framework
Shurgalina, Ekaterina; Gorshkov, Konstantin; Talipova, Tatiana; Pelinovsky, Efim
2016-04-01
As it is known the solitary waves (solitons) in the KdV-systems move with speed which exceeds the speed of propagation of long linear waves (sound speed). Due to interaction between them, solitons do not lose their individuality (elastic interaction). Binary interaction of neigborough solitons is the major contribution in the dynamics of soliton gas. Taking into account the integrability of the classic and modified Korteweg-de Vries equations the process of the soliton interaction can be analyzed in the framework of the rigorous analytical two-soliton solutions. Main physical conclusion from this solution is the phase shift which is positive for large solitons and negative for small solitons. This fact influences the average velocity of individual soliton in the soliton lattice or soliton gas. We demonstrate that soliton of relative small amplitude moves in soliton gas in average in opposite (negative) direction, meanwhile a free soliton moves always in the right direction. Approximated analytical theory is created for the soliton motion in the periodic lattice of big solitons of the same amplitudes, and the critical amplitude of the small soliton changed its averaged speed is found. Numerical simulation is conducted for a statistical assembly of solitons with random amplitudes and phases. The application of developed theory to the long surface and internal waves is discussed.
Multipole vector solitons in nonlocal nonlinear media.
Kartashov, Yaroslav V; Torner, Lluis; Vysloukh, Victor A; Mihalache, Dumitru
2006-05-15
We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.
Nonlinear electrodynamics in cytoskeletal protein lattices
Energy Technology Data Exchange (ETDEWEB)
Hameroff, S.R.; Smith, S.A.; Watt, R.C.
1983-01-01
Cytoskeletal lattice proteins including microtubules are particularly involved in dynamic regulation of intracellular movements and activities. This paper considers possibilities and implications of biological information processing due to coupling of Davydov solitons, Frohlich coherent oscillations and other nonlinear electrodynamic phenomena to conformational states of the grid-like polymer subunits of cytoskeletal microtubules. 39 references.
Spatial solitons in nonlinear liquid waveguides
Indian Academy of Sciences (India)
R Barillé; G Rivoire
2001-11-01
Spatial solitons are studied in a planar waveguide ﬁlled with nonlinear liquids. Spectral and spatial measurements for different geometries and input power of the laser beam show the inﬂuence of different nonlinear effects as stimulated scatterings on the soliton propagation and in particular on the beam polarization. The stimulated scattering can be used advantageously to couple the two polarization components. This effect can lead to multiple applications in optical switching.
Backward-wave propagation and discrete solitons in a left-handed electrical lattice
Energy Technology Data Exchange (ETDEWEB)
English, L.Q.; Wheeler, S.G. [Department of Physics and Astronomy, Dickinson College, Carlisle, PA 17013 (United States); Shen, Y. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Veldes, G.P. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece); Whitaker, N. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Kevrekidis, P.G., E-mail: kevrekid@math.umass.ed [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D.J. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece)
2011-02-28
We study experimentally, analytically and numerically the backward-wave propagation, and formation of discrete bright and dark solitons in a nonlinear electrical lattice. We observe experimentally that a focusing (defocusing) effect occurs above (below) a certain carrier frequency threshold, and backward-propagating bright (dark) discrete solitons are formed. We develop a discrete model emulating the relevant circuit and benchmark its linear properties against the experimental dispersion relation. Using a perturbation method, we derive a nonlinear Schroedinger equation, that predicts accurately the carrier frequency threshold. Finally, we use numerical simulations to corroborate our findings and monitor the space-time evolution of the discrete solitons.
Subwavelength Plasmonic Lattice Solitons in Arrays of Metallic Nanowires
Ye, Fangwei; Hu, Bambi; Panoiu, Nicolae C
2010-01-01
We predict theoretically that stable subwavelength plasmonic lattice solitons (PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear medium. The tight confinement of the guiding modes of the metallic nanowires, combined with the strong nonlinearity induced by the enhanced field at the metal surface, provide the main physical mechanisms for balancing the wave diffraction and the formation of PLSs. As the conditions required for the formation of PLSs are satisfied in a variety of plasmonic systems, we expect these nonlinear modes to have important applications to subwavelength nanophotonics. In particular, we show that the subwavelength PLSs can be used to optically manipulate with nanometer accuracy the power flow in ultracompact photonic systems.
Nonlinear soliton matching between optical fibers
DEFF Research Database (Denmark)
Agger, Christian; Sørensen, Simon Toft; Thomsen, Carsten L.
2011-01-01
In this Letter, we propose a generic nonlinear coupling coefficient, η2 NL ¼ ηjγ=β2jfiber2=jγ=β2jfiber1, which gives a quantitative measure for the efficiency of nonlinear matching of optical fibers by describing how a fundamental soliton couples from one fiber into another. Specifically, we use η...
Solitons and Weakly Nonlinear Waves in Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans
1985-01-01
Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...
Modulational stability and dark solitons in periodic quadratic nonlinear media
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....
Effect of interaction strength on gap solitons of Bose-Einstein condensates in optical lattices
Institute of Scientific and Technical Information of China (English)
Yang Ru-Shu; Yang Jiang-He
2008-01-01
We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose-Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose-Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose-Einstein condensate.
Spatiotemporal surface solitons in two-dimensional photonic lattices.
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2007-11-01
We analyze spatiotemporal light localization in truncated two-dimensional photonic lattices and demonstrate the existence of two-dimensional surface light bullets localized in the lattice corners or the edges. We study the families of the spatiotemporal surface solitons and their properties such as bistability and compare them with the modes located deep inside the photonic lattice.
Solitons in nonlocal nonlinear media: Exact solutions
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole
2001-01-01
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...
Ring vortex solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Briedis, D.; Petersen, D.E.; Edmundson, D.;
2005-01-01
or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....
A Hierarchy of Integrable Lattice Soliton Equations and New Integrable Symplectic Map
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure.A new integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method. The binary Bargmann constraint gives rise to a B(a)cklund transformation for the resulting integrable lattice equations. At last, conservation laws of the hierarchy are presented.
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
Lucian-Cornel Crasovan; Boris A Malomed; Dumitru Mihalache
2001-11-01
We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media.
Optical rogue waves and soliton turbulence in nonlinear fibre optics
DEFF Research Database (Denmark)
Genty, G.; Dudley, J. M.; de Sterke, C. M.
2009-01-01
We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....
Spiralling solitons and multipole localized modes in nonlocal nonlinear media
DEFF Research Database (Denmark)
Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan
2007-01-01
We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two differe...... models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form.......We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different...
Sivan, Y; Fibich, G; Ilan, B; Weinstein, M I
2008-10-01
We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multidimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to a focusing instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows one to predict the stability and instability strength.
The characters of nonlinear vibration in the two-dimensional discrete monoatomic lattice
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2005-01-01
The two-dimensional discrete monoatomic lattice is analyzed. Taking nearest-neighbor interaction into account, the characters of the nonlinear vibration in two-dimensional discrete monoatomic lattice are described by the two-dimensional cubic nonlinear Schrodinger equation. Considering the quartic nonlinear potential, the two-dimensional discrete-soliton trains and the solutions perturbed by the neck mode are presented.
Dipolar matter-wave solitons in two-dimensional anisotropic discrete lattices
Chen, Huaiyu; Liu, Yan; Zhang, Qiang; Shi, Yuhan; Pang, Wei; Li, Yongyao
2016-05-01
We numerically demonstrate two-dimensional (2D) matter-wave solitons in the disk-shaped dipolar Bose-Einstein condensates (BECs) trapped in strongly anisotropic optical lattices (OLs) in a disk's plane. The considered OLs are square lattices which can be formed by interfering two pairs of plane waves with different intensities. The hopping rates of the condensates between two adjacent lattices in the orthogonal directions are different, which gives rise to a linearly anisotropic system. We find that when the polarized orientation of the dipoles is parallel to disk's plane with the same direction, the combined effects of the linearly anisotropy and the nonlocal nonlinear anisotropy strongly influence the formations, as well as the dynamics of the lattice solitons. Particularly, the isotropy-pattern solitons (IPSs) are found when these combined effects reach a balance. Motion, collision, and rotation of the IPSs are also studied in detail by means of systematic simulations. We further find that these IPSs can move freely in the 2D anisotropic discrete system, hence giving rise to an anisotropic effective mass. Four types of collisions between the IPSs are identified. By rotating an external magnetic field up to a critical angular velocity, the IPSs can still remain localized and play as a breather. Finally, the influences from the combined effects between the linear and the nonlocal nonlinear anisotropy with consideration of the contact and/or local nonlinearity are discussed too.
Three-dimensional vortex solitons in quasi-two-dimensional lattices.
Leblond, Hervé; Malomed, Boris A; Mihalache, Dumitru
2007-08-01
We consider the three-dimensional (3D) Gross-Pitaevskii or nonlinear Schrödinger equation with a quasi-2D square-lattice potential (which corresponds to the optical lattice trapping a self-attractive Bose-Einstein condensate, or, in some approximation, to a photonic-crystal fiber, in terms of nonlinear optics). Stable 3D solitons, with embedded vorticity S=1 and 2, are found by means of the variational approximation and in a numerical form. They are built, basically, as sets of four fundamental solitons forming a rhombus, with phase shifts piS2 between adjacent sites, and an empty site in the middle. The results demonstrate two species of stable 3D solitons, which were not studied before, viz., localized vortices ("spinning light bullets," in terms of optics) with S>1 , and vortex solitons (with any S not equal 0 ) supported by a lattice in the 3D space. Typical scenarios of instability development (collapse or decay) of unstable localized vortices are identified too.
Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type.
Mayteevarunyoo, Thawatchai; Malomed, Boris A; Roeksabutr, Athikom
2011-08-29
Solitons in the model of nonlinear photonic crystals with the transverse structure based on two-dimensional (2D) quadratic- or rhombic-shaped Kronig-Penney (KP) lattices are studied by means of numerical methods. The model can also applies to a Bose-Einstein condensate (BEC) trapped in a superposition of linear and nonlinear 2D periodic potentials. The analysis is chiefly presented for the self-repulsive nonlinearity, which gives rise to several species of stable fundamental gap solitons, dipoles, four-peak complexes, and vortices in two finite bandgaps of the underlying spectrum. Stable solitons with complex shapes are found, in particular, in the second bandgap of the KP lattice with the rhombic structure. The stability of the localized modes is analyzed in terms of eigenvalues of small perturbations, and tested in direct simulations. Depending on the value of the KP's duty cycle (DC, i.e., the ratio of the void's width to the lattice period), an internal stability boundary for the solitons and vortices may exist inside of the first bandgap. Otherwise, the families of the localized modes are entirely stable or unstable in the bandgaps. With the self-attractive nonlinearity, only unstable solitons and vortices are found in the semi-infinite gap.
Vortex solitons at the interface separating square and hexagonal lattices
Energy Technology Data Exchange (ETDEWEB)
Jović Savić, Dragana, E-mail: jovic@ipb.ac.rs; Piper, Aleksandra; Žikić, Radomir; Timotijević, Dejan
2015-06-19
Vortex solitons at the interface separating two different photonic lattices – square and hexagonal – are demonstrated numerically. We consider the conditions for the existence of discrete vortex states at such interfaces and develop a concise picture of different scenarios of the vortex solutions behavior. Various vortices with different size and topological charges are considered, as well as various lattice interfaces. A novel type of discrete vortex surface solitons in a form of five-lobe solution is observed. Besides stable three-lobe and six-lobe discrete surface modes propagating for long distances, we observe various oscillatory vortex surface solitons, as well as dynamical instabilities of different kinds of solutions and study their angular momentum. Dynamical instabilities occur for higher values of the propagation constant, or at higher beam powers. - Highlights: • We demonstrate vortex solitons at the square–hexagonal photonic lattice interface. • A novel type of five-lobe surface vortex solitons is observed. • Different phase structures of surface solutions are studied. • Orbital angular momentum transfer of such solutions is investigated.
Dark Spatial Soliton Interaction in Nonlinear Kerr Medium
Institute of Scientific and Technical Information of China (English)
LuchuanWANG; QinliangFAN
1998-01-01
The dark spatial soliton interaction in nonlinear Kerr medium has been studied in this paper.The problem has been solved by the use of the slowly varying envelope approximation in solving coupled nonlinear Schroedinger equations.The perturbation nature of dark spatial soliton interaction has been described and some of their key properties has been discussed as well in the paper.
Self-induced gap solitons in nonlinear magnetic metamaterials.
Cui, Weina; Zhu, Yongyuan; Li, Hongxia; Liu, Sumei
2009-09-01
The self-induced gap solitons in nonlinear magnetic metamaterials is investigated. It is shown that the self-induced gap solitons may exist due to the interaction of the discreteness and nonlinearity. The evolution of these localized structures is studied in the phase plane and analytical and numerical expressions are obtained.
Anomalous interaction of nonlocal solitons in media with competing nonlinearities
DEFF Research Database (Denmark)
Esbensen, B. K.; Bache, Morten; Bang, Ole
2012-01-01
We theoretically investigate properties of individual bright spatial solitons and their interaction in nonlocal media with competing focusing and defocusing nonlinearities. We consider the general case with both nonlinear responses characterized by different strengths and degrees of nonlocality. We...... and interaction of solitons using numerical simulations of the full model of beam propagation. The numerical simulations fully confirm our analytical results....
Vector solitons in nonlinear isotropic chiral metamaterials
Tsitsas, N L; Frantzeskakis, D J
2011-01-01
Starting from the Maxwell equations, we used the reductive perturbation method to derive a system of two coupled nonlinear Schr\\"{o}dinger (NLS) equations for the two Beltrami components of the electromagnetic field propagating along a fixed direction in an isotropic nonlinear chiral metamaterial. With single-resonance Lorentz models for the permittivity and permeability and a Condon model for the chirality parameter, in certain spectral regimes, one of the two Beltrami components exhibits a negative real refractive index when nonlinearity is ignored and the chirality parameter is sufficiently large.We found that, inside such a spectral regime, there may exist a subregime wherein the system of the NLS equations can be approximated by the Manakov system. Bright-bright, dark-dark, and dark-bright vector solitons can be formed in that spectral subregime.
Vector solitons in nonlinear isotropic chiral metamaterials
Energy Technology Data Exchange (ETDEWEB)
Tsitsas, N L [School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografos, Athens 15773 (Greece); Lakhtakia, A [Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802-6812 (United States); Frantzeskakis, D J, E-mail: dfrantz@phys.uoa.gr [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece)
2011-10-28
Starting from the Maxwell equations, we used the reductive perturbation method to derive a system of two coupled nonlinear Schroedinger (NLS) equations for the two Beltrami components of the electromagnetic field propagating along a fixed direction in an isotropic nonlinear chiral metamaterial. With single-resonance Lorentz models for the permittivity and permeability and a Condon model for the chirality parameter, in certain spectral regimes, one of the two Beltrami components exhibits a negative-real refractive index when nonlinearity is ignored and the chirality parameter is sufficiently large. We found that, inside such a spectral regime, there may exist a subregime wherein the system of the NLS equations can be approximated by the Manakov system. Bright-bright, dark-dark, and dark-bright vector solitons can be formed in that spectral subregime. (paper)
Multi-soliton energy transport in anharmonic lattices
DEFF Research Database (Denmark)
Ostrovskaya, Elena A A.; Mingaleev, Serge F.; Kivshar, Yuri S S.;
2001-01-01
We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons (see Phys. Rev. Lett. 83 (1999) 296), our analysis reveals a novel...
Institute of Scientific and Technical Information of China (English)
Song Chang-Sheng; Li Jing; Zong Feng-De
2012-01-01
An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed.We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a timespace periodic optical lattice.The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations.A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate.We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. In this case,the analytical predictions of Bose-Einstein condensates variational dynamics are found to be in good agreement with numerical simulations.We then find a stable region for successful manipulating matter-wave solitons without collapse,which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice.
Institute of Scientific and Technical Information of China (English)
谢元栋
2012-01-01
Soliton excitation with high-oder-nonlinearity of spinor Bose-Einstein condensate in an optical lattice is studied in detail. The exact solution for bright soliton which is expressed as an elliptic integral is found, and the analytic solution for dark soliton with particular parameters is presented. The energy is also found.%研究了一维光格中旋量玻色-爱因斯坦凝聚体的高阶非线性作用下的孤子激发，得出了用椭圆积分表示的明孤子解和特定参数条件下的暗孤子解析解，并求得了能量表达式．
Dispersion managed solitons in the presence of saturated nonlinearity
Hundertmark, Dirk; Lee, Young-Ran; Ried, Tobias; Zharnitsky, Vadim
2017-10-01
The averaged dispersion managed nonlinear Schrödinger equation with saturated nonlinearity is considered. It is shown that under rather general assumptions on the saturated nonlinearity, the ground state solution corresponding to the dispersion managed soliton can be found for both zero residual dispersion and positive residual dispersion. The same applies to diffraction management solitons, which are a discrete version describing certain waveguide arrays.
Kevrekidis, P G; Saxena, A; Frantzeskakis, D J; Bishop, A R
2014-01-01
We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anti-continuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being what was considered as 1D bright solitons in the above-mentioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (analytically, whenever possible). Typical scenarios ...
Non-linear effects for cylindrical gravitational two-soliton
Tomizawa, Shinya
2015-01-01
Using a cylindrical soliton solution to the four-dimensional vacuum Einstein equation, we study non-linear effects of gravitational waves such as Faraday rotation and time shift phenomenon. In the previous work, we analyzed the single-soliton solution constructed by the Pomeransky's improved inverse scattering method. In this work, we construct a new two-soliton solution with complex conjugate poles, by which we can avoid light-cone singularities unavoidable in a single soliton case. In particular, we compute amplitudes of such non-linear gravitational waves and time-dependence of the polarizations. Furthermore, we consider the time shift phenomenon for soliton waves, which means that a wave packet can propagate at slower velocity than light.
The solitons redistribution in Bose-Einstein condensate in quasiperiodic optical lattice
Energy Technology Data Exchange (ETDEWEB)
Burlak, G.N. [Center for Research on Engineering and Applied Sciences, Autonomous State University of Morelos, Cuernavaca, Mor. 62210 (Mexico)], E-mail: gburlak@uaem.mx; Klimov, A.B. [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, Guadalajara, Jalisco 44420 (Mexico)], E-mail: klimov@cencar.udg.mx
2007-10-01
We numerically study the dynamical excitations in Bose-Einstein condensate (BEC) placed in periodic and quasiperiodic 2D optical lattice (OL). In case of the repulsive mean-field interaction the BEC quantum tunneling leads to a progressive soliton's splitting and generating of secondary solitons, which migrate to closest trapping potential minima. A nontrivial soliton dynamics appears when a series of {pi}-pulses (phase kicks) are applied to the optical lattice. Such sudden perturbation produces a dynamic redistribution of the secondary solitons, leading to a formation of an artificial solitonic superlattice. Different geometries of OL are analyzed.
Brazhnyi, Valeriy A
2011-01-01
We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schr\\"{o}dinger (DNLS) equation, including a local linear or nonlinear defect. Discrete solitons pinned to the defects are investigated by means of the numerical continuation from the anti-continuum limit and also using the variational approximation (VA), which features a good agreement for strongly localized modes. The models with the time-modulated strengths of the linear or nonlinear defect are considered too. In that case, one can temporarily shift the critical norm, below which localized 2D modes cannot exists, to a level above the norm of the given soliton, which triggers the irreversible delocalization transition.
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
Surface Plasmonic Lattice Solitons in Semi-infinite Graphene Sheet Arrays
Wang, Zhouqing; Long, Hua; Wang, Kai; Lu, Peixiang
2016-01-01
We investigate the surface plasmonic lattice solitons (PLSs) in semi-infinite graphene sheet arrays. The surface soliton is formed as the SPPs tunneling is inhibited by the graphene nonlinearity, and meanwhile the incident power should be above a threshold value. Thanks to the strong confinement of surface plasmon polaritons (SPPs) on graphene, the effective width of surface PLSs can be squeezed into deep-subwavelength scale of ~ 0.001{\\lambda}. Based on the stable propagation of surface PLSs, we find that the light propagation can be switched from the array boundary to the inner graphene sheets by reducing the incident power or increasing the chemical potential of graphene. The study may find promising application in optical switches on deep-subwavelength scale.
Institute of Scientific and Technical Information of China (English)
ZHOU Jun; XUE Chun-Hua; QI Yi-Hong; LOU Sen-Yue
2008-01-01
The properties of controllable soliton switching in Kerr-type optical lattices with different modulation are investigated theoretically and simulated numerically. The results show that the optical lattices can be available for all-optical soliton switching through utilization for length-scale competition effects. And through longitudinal exponential-asymptotic modulation for the linear refractive index, the properties of soliton switching in the optical lattices can be improved. The number of output channels of soliton switching can be controlled by the parameters such as incident angle, asymptotic rate of longitudinal modulation, guiding parameter and form factor.
Vectorial spatial solitons in bulk periodic quadratically nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Panoiu, N-C [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States); Mihalache, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Mazilu, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Lederer, F [Institute of Solid State Theory and Theoretical Optics, Friedrich Schiller University Jena, Max-Wien-Platz 1, Jena, D-07743 (Germany); Osgood, R M Jr [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States)
2004-05-01
We present a comprehensive analysis of the generation, propagation and characteristic properties of two-dimensional spatial solitons formed in quasi-phase-matched gratings through type-II vectorial interaction. By employing an averaging approach based on asymptotic expansion theory, we show that the dynamics of soliton propagation in the grating and their stability properties are strongly influenced by induced Kerr-like nonlinearities. Finally, through extensive numerical simulations, we verify the validity of our theoretical predictions.
Fundamental and vortex solitons in a two-dimensional optical lattice
Yang, J; Yang, Jianke; Musslimani, Ziad
2003-01-01
Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime, the fundamental soliton is largely confined to one lattice site, while the vortex state comprises of four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional vortex. However, in the weak localization regime, both the fundamental and vortex solitons spread over many lattice sites. We further show that fundamental and vortex solitons are stable against small perturbations in the strong localization regime.
Exact discrete soliton solutions of quintic discrete nonlinear Schr(o)dinger equation
Institute of Scientific and Technical Information of China (English)
Li Hua-Mei; Wu Feng-Min
2005-01-01
By using the extended hyperbolic function approach, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution,alternating phase bright soliton solution and alternating phase dark soliton solution, if a special constraint is imposed on the coefficients of the equation.
The Korteweg-de Vries soliton in the lattice hydrodynamic model
Ge, H. X.
2009-04-01
The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail in the car following model. So we devote ourselves to obtaining the KdV equation from the lattice hydrodynamic model and obtaining the KdV soliton solution describing the traffic jam. Numerical simulation is conducted, to demonstrate the nonlinear analysis result.
Tian, Qing; Wu, Lei; Zhang, Jie-Fang; Malomed, Boris A; Mihalache, D; Liu, W M
2011-01-01
We put forward a generic transformation which helps to find exact soliton solutions of the nonlinear Schrödinger equation with a spatiotemporal modulation of the nonlinearity and external potentials. As an example, we construct exact solitons for the defocusing nonlinearity and harmonic potential. When the soliton's eigenvalue is fixed, the number of exact solutions is determined by energy levels of the linear harmonic oscillator. In addition to the stable fundamental solitons, stable higher-order modes, describing array of dark solitons nested in a finite-width background, are constructed too. We also show how to control the instability domain of the nonstationary solitons.
Limiting amplitudes of fully nonlinear interfacial tides and solitons
Aguiar-González, Borja; Gerkema, Theo
2016-08-01
A new two-fluid layer model consisting of forced rotation-modified Boussinesq equations is derived for studying tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial waves. This set is a generalization of the Choi-Camassa equations, extended here with forcing terms and Coriolis effects. The forcing is represented by a horizontally oscillating sill, mimicking a barotropic tidal flow over topography. Solitons are generated by a disintegration of the interfacial tide. Because of strong nonlinearity, solitons may attain a limiting table-shaped form, in accordance with soliton theory. In addition, we use a quasi-linear version of the model (i.e. including barotropic advection but linear in the baroclinic fields) to investigate the role of the initial stages of the internal tide prior to its nonlinear disintegration. Numerical solutions reveal that the internal tide then reaches a limiting amplitude under increasing barotropic forcing. In the fully nonlinear regime, numerical experiments suggest that this limiting amplitude in the underlying internal tide extends to the nonlinear case in that internal solitons formed by a disintegration of the internal tide may not reach their table-shaped form with increased forcing, but appear limited well below that state.
Breatherlike impurity modes in discrete nonlinear lattices
DEFF Research Database (Denmark)
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Statics characteristics of two Bose-Einstein condensate dark solitons trapped in an optical lattice
Institute of Scientific and Technical Information of China (English)
CHENG Yong-shan; GONG Rong-zhou; LI Hong
2006-01-01
The statics characteristics of two coupled Bose-Einstein condensate (BEC) dark solitons trapped in an optical lattice are investigated with the variational approach.It is found that the interaction between a ‘kink’ and an ‘anti-kink’ with opposite phase gradients is effectively repulsive, and the optical lattice can be controllably used to produce a pair of static BEC dark solitons.Its effect depends on the initial location of the BEC dark solitons, the lattice amplitude and wave number.
Zeno effect and switching of solitons in nonlinear couplers
DEFF Research Database (Denmark)
Abdullaev, F Kh; Konotop, V V; Ögren, Magnus;
2011-01-01
The Zeno effect is investigated for soliton type pulses in a nonlinear directional coupler with dissipation. The effect consists in increase of the coupler transparency with increase of the dissipative losses in one of the arms. It is shown that localized dissipation can lead to switching...
Solitons supported by singular spatial modulation of the Kerr nonlinearity
Borovkova, Olga V; Malomed, Boris A
2012-01-01
We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the uniform self-defocusing (SDF) nonlinear background, and with a similar singular repulsive linear potential. The setting, which can be implemented in optics and BEC, aims to extend the general analysis of the existence and stability of solitons in NLSEs. Results for fundamental solitons are obtained analytically and verified numerically. The solitons feature a quasi-cuspon shape, with the second derivative diverging at the center, and are stable in the entire existence range, which is 0 < a < 1. Dipole (odd) solitons are found too. They are unstable in the infinite domain, but stable in the semi-infinite one. In the presence of the SDF background, there are two subfamilies of fundamental solitons, one stable and one unstable, which exist together above a threshold value ...
Chiral Edge Mode in the Coupled Dynamics of Magnetic Solitons in a Honeycomb Lattice
Kim, Se Kwon; Tserkovnyak, Yaroslav
2017-08-01
Motivated by a recent experimental demonstration of a chiral edge mode in an array of spinning gyroscopes, we theoretically study the coupled gyration modes of topological magnetic solitons, vortices and magnetic bubbles, arranged as a honeycomb lattice. The soliton lattice under suitable conditions is shown to support a chiral edge mode like its mechanical analogue, the existence of which can be understood by mapping the system to the Haldane model for an electronic system. The direction of the chiral edge mode is associated with the topological charge of the constituent solitons, which can be manipulated by an external field or by an electric-current pulse. The direction can also be controlled by distorting the honeycomb lattice. Our results indicate that the lattices of magnetic solitons can serve as reprogrammable topological metamaterials.
Institute of Scientific and Technical Information of China (English)
LIU Chun-Ping; LING Zhi
2005-01-01
By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified way. When the module m → 1, these solutions exactly degenerate to the soliton solutions of the equations. Then we reveal the relationship between the soliton-like solutions obtained by other authors and these soliton solutions of the equations.
Rotating soliton clusters in nonlocal nonlinear media
Institute of Scientific and Technical Information of China (English)
Wang Yu-Qing; Guo Qi
2008-01-01
From the study of the dynamics for the ring-like soliton clusters, we find that there exists a critical value of the ring radius, dcr, for the stationary rotation of the clusters with respect to the beam centre even in the presence of the relatively strong noise, and that the soliton clusters will not rotate but only undergo periodic collisions in the form of simple harmonic oscillator if the ring radius is large enough. We also show that the direction of the rotation can be opposite to the direction of phase gradient when the relative phase difference is within the domain 0<|θ|<π, while along the direction of phase gradient when the relative phase difference is within the domain π<|θ|<2π.
Two-Dimensional Anharmonic Crystal Lattices: Solitons, Solectrons, and Electric Conduction
Velarde, Manuel G.; Ebeling, Werner; Chetverikov, Alexander P.
2011-01-01
Reported here are salient features of soliton-mediated electron transport in anharmonic crystal lattices.After recalling how an electron-soliton bound state (solectron) can be formed we comment on consequences like electron surfing on a sound wave and balistic transport, possible percolation in 2d lattices, and a novel form of electron pairing with strongly correlated electrons both in real space and momentum space.
Soliton gyroscopes in media with spatially growing repulsive nonlinearity
Driben, Rodislav; Malomed, Boris A; Meier, Torsten; Torner, Lluis
2013-01-01
We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S. The family with S=1 is completely stable, while the one with S=2 has alternating regions of stability and instability. The families are nearly exactly reproduced in an analytical form by the Thomas-Fermi approximation (TFA). Unstable states with S=2 and 3 split into persistently rotating pairs or triangles of unitary vortices. Application of a moderate torque to the vortex torus initiates a persistent precession mode, with the torus' axle moving along a conical surface. A strong torque heavily deforms the vortex solitons, but, nonetheless, they restore themselves with the axle oriented according to the vectorial addition of angular momenta.
Trullinger, SE; Pokrovsky, VL
1986-01-01
In the twenty years since Zabusky and Kruskal coined the term ``soliton'', this concept changed the outlook on certain types of nonlinear phenomena and found its way into all branches of physics. The present volume deals with a great variety of applications of the new concept in condensed-matter physics, which is particularly reached in experimentally observable occurrences. The presentation is not centred around the mathematical aspects; the emphasis is on the physical nature of the nonlinear phenomena occurring in particular situations.With its emphasis on concrete, mostly experime
Chen, Qian-Yong; Malomed, Boris A
2011-01-01
We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schr\\"{o}dinger equation (NLSE), which includes the harmonic-oscillator (HO) potential and a random potential. The equation models experimentally relevant spatially disordered settings in Bose-Einstein condensates (BECs) and nonlinear optics. First, the generation of soliton arrays from a broad initial quasi-uniform state by the modulational instability (MI) is considered, following a sudden switch of the nonlinearity from repulsive to attractive. Then, we study oscillations of a single soliton in this setting, which models a recently conducted experiment in BEC. Basic characteristics of the MI-generated array, such as the number of solitons and their mobility, are reported as functions of the strength and correlation length of the disorder, and of the total norm. For the single oscillating soliton, its survival rate is found. Main features of these dependences are explained qualitatively.
Stabilization of solitons under competing nonlinearities by external potentials
Energy Technology Data Exchange (ETDEWEB)
Zegadlo, Krzysztof B., E-mail: zegadlo@if.pw.edu.pl; Karpierz, Miroslaw A. [Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa (Poland); Wasak, Tomasz; Trippenbach, Marek [Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa (Poland); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-12-15
We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.
Institute of Scientific and Technical Information of China (English)
NIU Jia-Sheng; MA Ben-Kun
2003-01-01
In this paper, we theoretically discuss the soliton properties of light pulse transportation on the surface of an ionic crystal having strong nonlinear interactions between ions of unit cells. We analyze in detail the dark solitons when the nonlinear coefficient g is positive and negative, respectively. It is found that whether the nonlinear coefficient g is positive or negative, the dark solitons can be formed over the whole dispersion relation area of surface polaritons considering nonlinear effects. Attention should be paid to the fact that around ωTO, the light pulse can form advanced dark solitons, and there is a switching area from advanced dark soliton to retarded dark soliton near ωTO. We also discuss the effects of higher nonlinear dispersion on the solitons.
Transition from Solitons to Solitary Waves in the Fermi-Pasta-Ulam Lattice
Wen, Zhenying; Wei, Nian
2016-01-01
In this paper, we study the smooth transition from solitons to solitary waves in localization, relation between energy and velocity, propagation and scattering property in the Fermi-Pasta-Ulam lattice analytically and numerically. A soliton is a very stable solitary wave that retains its permanent structure after interacting with other solitary waves. A soliton exists when the energy is small, and it becomes a solitary wave when the energy increases to the threshold. The transition could help to understand the distinctly different heat conduction behaviors of the Fermi-Pasta-Ulam lattice at low and high temperature.
Evolution of soliton-like train in Klein-Gordon lattice system
Institute of Scientific and Technical Information of China (English)
Xia Qing-Lin; Yi Jian-Hong; Peng Yuan-Dong; Ye Tu-Ming; Li Li-Ya; Wang Hong-Zhong
2007-01-01
This paper studies the evolution of wave in the system of a pure anharmonic lattice with a double well on-site potential by numerical calculation. It finds that an initial distribution of static or moving wave can evolve into two travelling soliton-like trains with contrary directions and a region of oscillation in this lattice system. It presents that some cases with cosine-square-shape and Gaussian-shape initial distribution of static or moving wave will produce ordered soliton-like train. Careful numerical observation shows that the centre oscillation region in this system may act as a resource of generating soliton-like train.
Supersymmetric quantum mechanics approach to a nonlinear lattice
Energy Technology Data Exchange (ETDEWEB)
Ricotta, Regina Maria [Faculdade de Tecnologia de Sao Paulo (FATEC), SP (Brazil); Drigo Filho, Elso [Universidade Estadual Paulista Julio de Mesquita Filho (UNESP), SP (Brazil)
2011-07-01
Full text: DNA is one of the most important macromolecules of all biological system. New discoveries about it have open a vast new field of research, the physics of nonlinear DNA. A particular feature that has attracted a lot of attention is the thermal denaturation, i.e., the spontaneous separation of the two strands upon heating. In 1989 a simple lattice model for the denaturation of the DNA was proposed, the Peyrard-Bishop model, PB. The bio molecule is described by two chains of particles coupled by nonlinear springs, simulating the hydrogen bonds that connect the two basis in a pair. The potential for the hydrogen bonds is usually approximated by a Morse potential. The Hamiltonian system generates a partition function which allows the evaluation of the thermodynamical quantities such as mean strength of the basis pairs. As a byproduct the Hamiltonian system was shown to be a NLSE (nonlinear Schroedinger equation) having soliton solutions. On the other hand, a reflectionless potential with one bound state, constructed using supersymmetric quantum mechanics, SQM, can be shown to be identical to a soliton solution of the KdV equation. Thus, motivated by this Hamiltonian problem and inspired by the PB model, we consider the Hamiltonian of a reflectionless potential through SQM, in order to evaluate thermodynamical quantities of a unidimensional lattice with possible biological applications. (author)
Kengne, E; Lakhssassi, A
2015-03-01
We consider a lossless one-dimensional nonlinear discrete bi-inductance electrical transmission line made of N identical unit cells. When lattice effects are considered, we use the reductive perturbation method in the semidiscrete limit to show that the dynamics of modulated waves can be modeled by the classical nonlinear Schrödinger (CNLS) equation, which describes the modulational instability and the propagation of bright and dark solitons on a continuous-wave background. Our theoretical analysis based on the CNLS equation predicts either two or four frequency regions with different behavior concerning the modulational instability of a plane wave. With the help of the analytical solutions of the CNLS equation, we investigate analytically the effects of the linear capacitance CS on the dynamics of matter-wave solitons in the network. Our results reveal that the linear parameter CS can be used to manipulate the motion of bright, dark, and kink soliton in the network.
Directory of Open Access Journals (Sweden)
Daohong Song
2012-01-01
Full Text Available We provide a brief overview on our recent experimental work on linear and nonlinear localization of singly charged vortices (SCVs and doubly charged vortices (DCVs in two-dimensional optically induced photonic lattices. In the nonlinear case, vortex propagation at the lattice surface as well as inside the uniform square-shaped photonic lattices is considered. It is shown that, apart from the fundamental (semi-infinite gap discrete vortex solitons demonstrated earlier, the SCVs can self-trap into stable gap vortex solitons under the normal four-site excitation with a self-defocusing nonlinearity, while the DCVs can be stable only under an eight-site excitation inside the photonic lattices. Moreover, the SCVs can also turn into stable surface vortex solitons under the four-site excitation at the surface of a semi-infinite photonics lattice with a self-focusing nonlinearity. In the linear case, bandgap guidance of both SCVs and DCVs in photonic lattices with a tunable negative defect is investigated. It is found that the SCVs can be guided at the negative defect as linear vortex defect modes, while the DCVs tend to turn into quadrupole-like defect modes provided that the defect strength is not too strong.
Surface defect gap solitons in one-dimensional dual-frequency lattices
Institute of Scientific and Technical Information of China (English)
Zhu Wei-Ling; Luo Li; He Ying-Ji; Wang He-Zhou
2009-01-01
We study the surface defect gap solitons in an interface between a defect of one-dimensional dual-frequency lattices and the uniform media. Some unique properties are revealed that such lattices can broaden the region of semi-finite gap, and the semi-finite gap exists not only in the positive and zero defects but also in the negative defect; unlike in the regular lattices, the semi-finite gap exists in the positive and zero defects but does not exist in the negative defect. In particular, stable solitons exist almost in the whole semi-finite gap for the positive and zero defects. These properties are different from other lattices with defects. In addition. it is found that the existence of surface dual-frequency lattice solitons does not need a threshold Power.
Transmutation of skyrmions to half-solitons driven by the nonlinear optical spin Hall effect.
Flayac, H; Solnyshkov, D D; Shelykh, I A; Malpuech, G
2013-01-04
We show that the spin domains, generated in the linear optical spin Hall effect by the analog of spin-orbit interaction for exciton polaritons, are associated with the formation of a Skyrmion lattice. In the nonlinear regime, the spin anisotropy of the polariton-polariton interactions results in a spatial compression of the domains and in a transmutation of the Skyrmions into oblique half-solitons. This phase transition is associated with both the focusing of the spin currents and the emergence of a strongly anisotropic emission pattern.
Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation
Moon, H. T.; Goldman, M. V.
1984-01-01
The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.
Energy Technology Data Exchange (ETDEWEB)
Wang Dengshan [CEMA and CIAS, Central Univ. of Finance and Economics, BJ (China); BNLCMP, Inst. of Physics, Chinese Academy of Sciences, BJ (China); Liu Yifang [School of Economics, Central Univ. of Finance and Economics, BJ (China)
2010-01-15
In this paper, with the aid of symbolic computation the bright soliton solutions of two variable-coefficient coupled nonlinear Schroedinger equations are obtained by Hirota's method. Some figures are plotted to illustrate the properties of the obtained solutions. The properties are meaningful for the investigation on the stability of soliton propagation in the optical soliton communications. (orig.)
Leblond, Hervé; Mihalache, Dumitru; 10.1103/PHYSREVA.80.053812
2011-01-01
By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given.
Stabilization of solitons under competing nonlinearities by external potentials
Zegadlo, Krzysztof B; Malomed, Boris A; Karpierz, Miroslaw A; Trippenbach, Marek
2014-01-01
We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates (BEC) loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations (VA and TFA), and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of com...
Soliton states of Maxwell’s equations and nonlinear Schrodinger equation
Institute of Scientific and Technical Information of China (English)
陈翼强
1997-01-01
Similarities and fundamental differences between Maxwell’s equations and nonlinear Schrodinger equation in predicting a soliton evolution in a uniform nonlinear anisotropic medium are analyzed.It is found that in some cases,the soliton solutions to the nonlinear Schrodinger equation cannot be recovered from Maxwell’s equations while in others the soliton solutions to Maxwell’s equations are lost from the nonlinear Schrodinger equation through approximation,although there are cases where the soliton solutions to the two sets of the equations demonstrate only quantitative difference.The origin of the differences is also discussed.
Nonlinear shallow ocean-wave soliton interactions on flat beaches.
Ablowitz, Mark J; Baldwin, Douglas E
2012-09-01
Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.
Nonlinear plasmonic amplification via dissipative soliton-plasmon resonances
Ferrando, Albert
2017-01-01
In this contribution we introduce a strategy for the compensation of plasmonic losses based on a recently proposed nonlinear mechanism: the resonant interaction between surface plasmon polaritons and spatial solitons propagating in parallel along a metal/dielectric/Kerr structure. This mechanism naturally leads to the generation of a quasiparticle excitation, the so-called soliplasmon resonance. We analyze the role played by the effective nonlinear coupling inherent to this system and how this can be used to provide a mechanism of quasiresonant nonlinear excitation of surface plasmon polaritons. We will pay particular attention to the introduction of asymmetric linear gain in the Kerr medium. The unique combination of nonlinear propagation, nonlinear coupling, and gain give rise to a scenario for the excitation of long-range surface plasmon polaritons with distinguishing characteristics. The connection between plasmonic losses and soliplasmon resonances in the presence of gain will be discussed.
Institute of Scientific and Technical Information of China (English)
Wenhua Cao; Songhao Liu
2005-01-01
Stable picosecond soliton transmission is demonstrated numerically by use of concatenated gain-distributed nonlinear amplifying fiber loop mirrors (NALMs). We show that, as compared with previous soliton transmission schemes that use conventional NALMs or nonlinear optical loop mirror (NOLM) and amplifier combinations, the present scheme permits significant increase of loop-mirror (amplifier) spacing. The broad switching window of the present device and the high quality pulses switched from it provide a reasonable stability range for soliton transmission. Soliton-soliton interactions can be reduced efficiently by using lowly dispersive fibers.
Coupled Modified Korteweg-de Vries Lattice in (2+1) Dimensions and Soliton Solutions
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The coupled semi-discrete modified Korteweg-de Vries equation in (2+1)-dimensions is proposed. It is shown that it can be decomposed into two (1+1)-dimensional differential-difference equations belonging to mKdV lattice hierarchy by considering a discrete isospectral problem. A Darboux transformation is set up for the resulting (2+1)- dimensional lattice soliton equation with the help of gauge transformations of Lax pairs. As an illustration by example,the soliton solutions of the mKdV lattice equation in (2+1)-dimensions are explicitly given.
Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations
Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Liu, Yi; Grelu, Philippe
2016-06-01
We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viable for both the focusing and defocusing Kerr nonlinearities, could exhibit an extra doubly localized chirp while keeping the characteristic intensity features of the original Peregrine soliton, hence the term chirped Peregrine soliton. The existence of chirped Peregrine solitons in a self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order dispersion. We numerically confirm the robustness of such chirped Peregrine solitons in spite of the onset of modulation instability.
Multi-soliton rational solutions for some nonlinear evolution equations
Directory of Open Access Journals (Sweden)
Osman Mohamed S.
2016-01-01
Full Text Available The Korteweg-de Vries equation (KdV and the (2+ 1-dimensional Nizhnik-Novikov-Veselov system (NNV are presented. Multi-soliton rational solutions of these equations are obtained via the generalized unified method. The analysis emphasizes the power of this method and its capability of handling completely (or partially integrable equations. Compared with Hirota’s method and the inverse scattering method, the proposed method gives more general exact multi-wave solutions without much additional effort. The results show that, by virtue of symbolic computation, the generalized unified method may provide us with a straightforward and effective mathematical tool for seeking multi-soliton rational solutions for solving many nonlinear evolution equations arising in different branches of sciences.
Institute of Scientific and Technical Information of China (English)
ZhangTiande; CaoQingjie; PriceG.W.; DjidjeliK.; TwizellE.H.
1999-01-01
Spatial soliton solutions of a class of generalized nonlinear Schrodinger equations in N-space are discussed analytically and numerically. This achieved using a traveling wavemethod to formulate one-soliton solution and the P-R method is employed to the numerlcal solutions and the interactions between the solirons for the generalized nonlinear systems in Z-pace.The results presented show that the soliton phenomena are characteristics associated with the nonlinearhies of the dynamical systems.
Bright Chirp-free and Chirped Nonautonomous solitons under Dispersion and Nonlinearity Management
Yang, Zhan-Ying; Zhang, Tao; Yue, Rui-Hong
2011-01-01
We present a series of chirp-free and chirped analytical nonautonomous soliton solutions to the generalized nonlinear Schrodinger equation (NLSE) with distributed coefficients by Darboux transformation from a trivial seed. For chirpfree nonautonomous soliton, the dispersion management term can change the motion of nonautonomous soliton and do not affect its shape at all. Especially,the classical optical soliton can be presented with variable dispersion term and nonlinearity when there is no gain. For chirped nonautonomous soliton, dispersion management can affect the shape and motion of nonautonomous solitons meanwhile. The periodic dispersion term can be used to control its "breathing" shape, and it does not affect the trajectory of nonautonomous soliton center with a certain condition.
Indian Academy of Sciences (India)
HONG-YU WU; LI-HONG JIANG
2017-09-01
From a generic transformation, a $(3+1)$-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter $m = 0$, Gaussian solitons are constructed. For the modulation depth $q = 1$ and the azimuthal parameter $m \
Wu, Hong-Yu; Jiang, Li-Hong
2017-09-01
From a generic transformation, a (3+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter m = 0, Gaussian solitons are constructed. For the modulation depth q = 1 and the azimuthal parameter m\
Institute of Scientific and Technical Information of China (English)
Liu Xiao-Bei; Li Biao
2011-01-01
We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schr(o)dinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters.Different shapes of bright solitons,a train of bright solitons and dark solitons are observed.The obtained results may raise the possibilities of relevant experiments and potential applications.
Vortices and ring dark solitons in nonlinear amplifying waveguides
Zhang, Jie-Fang; Li, Lu; Mihalache, Dumitru; Malomed, Boris A
2010-01-01
We consider the generation and propagation of (2+1)-dimensional beams in a nonlinear waveguide with the linear gain. Simple self-similar evolution of the beams is achieved at the asymptotic stage, if the input beams represent the fundamental mode. On the contrary, if they carry vorticity or amplitude nodes (or phase slips), vortex tori and ring dark solitons (RDSs) are generated, featuring another type of the self-similar evolution, with an exponentially shrinking vortex core or notch of the RDS. Numerical and analytical considerations reveal that these self-similar structures are robust entities in amplifying waveguides, being \\emph{stable} against azimuthal perturbations.
Evolutions of matter-wave bright soliton with spatially modulated nonlinearity
Institute of Scientific and Technical Information of China (English)
Yongshan Cheng; Fei Liu
2009-01-01
The evolution characteristics of a matter-wave bright soliton are investigated by means of the variational approach in the presence of spatially varying nonlinearity.It is found that the atom density envelope of the soliton is changed as a result of the spatial variation of the s-wave scattering length.The stable soliton can exist in appropriate initial conditions.The movement of the soliton depends on the sign and value of the coefficient of spatially modulated nonlinearity.These theoretical predictions are confirmed by the full numerical simulations of the one-dimensional Gross-Pitaevskii equation.
Energy Technology Data Exchange (ETDEWEB)
Wang, Pan [State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876 (China); Tian, Bo, E-mail: tian.bupt@yahoo.com.cn [State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876 (China); Jiang, Yan; Wang, Yu-Feng [State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876 (China)
2013-02-15
For describing the dynamics of alpha helical proteins with internal molecular excitations, nonlinear couplings between lattice vibrations and molecular excitations, and spin excitations in one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin with the octupole–dipole interactions, we consider an inhomogeneous generalized fourth-order nonlinear Schrödinger equation. Based on the Ablowitz–Kaup–Newell–Segur system, infinitely many conservation laws for the equation are derived. Through the auxiliary function, bilinear forms and N-soliton solutions for the equation are obtained. Interactions of solitons are discussed by means of the asymptotic analysis. Effects of linear inhomogeneity on the interactions of solitons are also investigated graphically and analytically. Since the inhomogeneous coefficient of the equation h=α x+β, the soliton takes on the parabolic profile during the evolution. Soliton velocity is related to the parameter α, distance scale coefficient and biquadratic exchange coefficient, but has no relation with the parameter β. Soliton amplitude and width are only related to α. Soliton position is related to β.
Soliton pair generation in the interactions of Airy and nonlinear accelerating beams
Zhang, Yiqi; Wu, Zhenkun; Zheng, Huaibin; Lu, Keqing; Li, Yuanyuan; Zhang, Yanpeng
2013-01-01
We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not.
Bipolar solitons of the focusing nonlinear Schrödinger equation
Liu, Zhongxuan; Feng, Qi; Lin, Chengyou; Chen, Zhaoyang; Ding, Yingchun
2016-11-01
The focusing nonlinear Schrödinger equation (NLSE) is a universal model for studying solitary waves propagation in nonlinear media. The NLSE is especially important in understanding how solitons on a condensate background (SCB) appear from a small perturbation through modulation instability. We study theoretically the one- and two-soliton solutions of the NLSE in presence of a condensate by using the dressing method. It is found that a class of bipolar elliptically polarized solitons with the choice of specific parameters in the one- and two-soliton solutions. Collisions among these solitons are studied by qualitative analysis and graphical illustration. We also generalize the concept of the quasi-Akhmediev breather to the bipolar solitons and show how it can be used for wave profile compression down to the extremely short duration. Our results extend previous studies in this area of the SCB and play an important role in the theory of freak wave.
Bipolar solitons of the focusing nonlinear Schrödinger equation
Energy Technology Data Exchange (ETDEWEB)
Liu, Zhongxuan, E-mail: 13237379393@163.com; Feng, Qi; Lin, Chengyou; Chen, Zhaoyang; Ding, Yingchun, E-mail: dingyc@mail.buct.edu.cn
2016-11-15
The focusing nonlinear Schrödinger equation (NLSE) is a universal model for studying solitary waves propagation in nonlinear media. The NLSE is especially important in understanding how solitons on a condensate background (SCB) appear from a small perturbation through modulation instability. We study theoretically the one- and two-soliton solutions of the NLSE in presence of a condensate by using the dressing method. It is found that a class of bipolar elliptically polarized solitons with the choice of specific parameters in the one- and two-soliton solutions. Collisions among these solitons are studied by qualitative analysis and graphical illustration. We also generalize the concept of the quasi-Akhmediev breather to the bipolar solitons and show how it can be used for wave profile compression down to the extremely short duration. Our results extend previous studies in this area of the SCB and play an important role in the theory of freak wave.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)
2014-02-15
We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinear Schroedinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinear Schroedinger equation generalized by including a nonlocal nonlinear term, we calculate four different physical quantities as a function of time, which are the return probability to the initial excitation site, the participation number, the root-mean-square displacement from the excitation site and the spatial probability distribution. We investigate the influence of the nonlocal nonlinearity on the delocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trapping region, we find that the nonlocal nonlinearity compresses the soliton width and slows down the spreading of the wave packet. In the vicinity of the delocalization to self-trapping transition point and inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which we call partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.
Two-dimensional lattice solitons in polariton condensates with spin-orbit coupling
Kartashov, Yaroslav V
2016-01-01
We study two-dimensional fundamental and vortex solitons in polariton condensates with spin-orbit coupling and Zeeman splitting evolving in square arrays of microcavity pillars. Due to repulsive excitonic nonlinearity such states are encountered in finite gaps in the spectrum of the periodic array. Spin-orbit coupling between two polarization components stemming from TE-TM energy splitting of the cavity photons acting together with Zeeman splitting lifts the degeneracy between vortex solitons with opposite topological charges and makes their density profiles different for a fixed energy. This results in formation of four distinct families of vortex solitons with topological charges m=+-1, all of which can be stable. At the same time, only two stable families of fundamental gap solitons characterized by domination of different polarization components are encountered.
On the reflection of solitons of the cubic nonlinear Schrödinger equation
Katsaounis, Theodoros
2016-07-05
In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the underlying mathematical model, and we use an implicit-explicit type Crank-Nicolson finite element scheme for its numerical solution. After verifying the perfect reflection of the solitons on a vertical wall, we present the imperfect reflection of a dark soliton on a diagonal wall.
Dipole Solitons in Nonlinear Media with an Exponential-Decay Nonlocal Response
Institute of Scientific and Technical Information of China (English)
YANG Zhen-Jun; MA Xue-Kai; ZHENG Yi-Zhou; GAO Xing-Hui; LU Da-Quan; HU Wei
2011-01-01
By applying the variational approach,the analytical expression of dipole solitons is obtained in nonlinear media with an exponential-decay nonlocal response.The relations of the soliton power versus the propagation constant and the soliton width are given.Some numerical simulations are carried out.The results show that the analytical expression is in excellent agreement with the numerical results for the strongly nonlocal case.
Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
Indian Academy of Sciences (India)
Hitender Kumar; Anand Malik; Fakir Chand
2013-02-01
In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.
Hernández-Tenorio, C.; Serkin, V. N.; Belyaeva, T. L.; Peña-Moreno, R.; Morales-Lara, L.
2015-01-01
The nonlinear Schrödinger equation (NLSE) model with an external harmonic potential is one of the most important in modern science. This model makes it possible to analyze a variety of nonlinear phenomena, in nonlinear optics and laser physics, biophysics and in the theory of Bose-Einstein condensation of atoms. It is shown that the main specific feature of the dynamics of dark GP matter wave solitons in a parabolic trap is the formation of solitons with dynamically changing form-factors producing the periodic variation in the modulation depth (the degree of "blackness") of dark solitons. In general, the period of dark soliton oscillations in trapping potential depends on the specific conditions of the experiment and does not coincide with the oscillation period of a linear quantum-mechanical oscillator. In the case of an immobile pedestal in the trap, the oscillation period of the black soliton considerably increases because of the periodic transformation of the black soliton to the gray one and vice versa. Surprisingly, that if the dark soliton is superimposed on the base pedestal oscillating in the trap and displaced from the trap center, the oscillation period of the dark soliton coincides with the period of oscillations of the linear harmonic oscillator, while the dynamics of the dark soliton is similar to that of a classical particle obeying the Newton mechanics laws.
Analytical solitons for Langmuir waves in plasma physics with cubic nonlinearity and perturbations
Energy Technology Data Exchange (ETDEWEB)
Zhou, Qin [Wuhan Donghu Univ. (China). School of Electronics and Information Engineering; Mirzazadeh, M. [Guilan Univ. (Iran, Islamic Republic of). Dept. of Engineering Sciences
2016-07-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schroedinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
Analytical Solitons for Langmuir Waves in Plasma Physics with Cubic Nonlinearity and Perturbations
Zhou, Qin; Mirzazadeh, M.
2016-09-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schrödinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
Trofimov, Vyacheslav A.; Lysak, T. M.
2016-05-01
We demonstrate a new possibility of a soliton velocity control at its propagation in a nonlinear layered structure (1D photonic crystal) which is placed in a nonlinear ambient medium. Nonlinear response of the ambient medium, as well as the PhC layers, is cubic. At the initial time moment, a soliton is spread over a few layers of PhC. Then, soliton propagates across the layered structure because of the initial wave-vector direction presence for the laser beam. The soliton reaches the PhC faces and reflects from them or passes through the face. As a nonlinear medium surrounds the PhC, the laser beam obtains additional impulse after interaction with this medium and accelerates (or slows down or stops near the PhC face). Nonlinear response of the ambient medium can be additionally created by another laser beam which shines near the PhC faces.
Soliton-plasma nonlinear dynamics in mid-IR gas-filled hollow-core fibers
DEFF Research Database (Denmark)
Habib, Selim; Markos, Christos; Bang, Ole
2017-01-01
We investigate numerically soliton-plasma interaction in a noble-gas-filled silica hollow-core anti-resonant fiber pumped in the mid-IR at 3.0 mu m. We observe multiple soliton self-compression stages due to distinct stages where either the self-focusing or the self-defocusing nonlinearity...... dominates. Specifically, the parameters may be tuned so the competing plasma self-defocusing nonlinearity only dominates over the Kerr self-focusing nonlinearity around the soliton self-compression stage, where the increasing peak intensity on the leading pulse edge initiates a competing self...
Finite-Length Soliton Solutions of the Local Homogeneous Nonlinear Schrödinger Equation
Caparelli, E C; Mizrahi, S S
1998-01-01
We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schrödinger equation. In contradistinction to the "usual'' solitons like are nonanalytical functions with continuous first derivatives, which are different from zero only inside some finite regions of space. The simplest one-dimensional example is the function which is equal to identically equal to zero for |x-kt|>\\pi/(2g). The FLS exist even in the case of a weak nonlinearity, whereas the ``usual'' solitons exist provided the nonlinearity parameters surpass some critical values.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, J [Departamento de Matematicas, E T S de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), Avda Camilo Jose Cela, 3 Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain); Cuevas, J [Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Universitaria Politecnica, C/Virgen de Africa, 7, 41011 Sevilla (Spain)], E-mail: juan.belmonte@uclm.es, E-mail: jcuevas@us.es
2009-04-24
In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic-quintic nonlinear Schroedinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose-Einstein condensates and nonlinear optics.
Optical Soliton Propagation in a Free-Standing Nonlinear Graphene Monolayer with Defects
Moxley, Frederick Ira; Radadia, Adarsh; Dai, Weizhong
2013-01-01
Recently, optical soliton propagation in an intrinsic nonlinear graphene monolayer configuration has been discovered. However, optical soliton behavior in a free-standing graphene monolayer with defects has not yet been studied. The objective of this article is to employ the generalized finite- difference time-domain (G-FDTD) method to efficiently simulate bright optical solitons, illustrating propagation of the electric field distribution in a free-standing nonlinear layer with variation in nonlinearity along its width. These variations of nonlinearity along the width represent graphene impurities, or defects. Results show that solitons propagate effectively even in the presence of strong spatial variations in the nonlinearity, implying the robustness of the medium with respect to optical propagation.
Discrete Nonlinear Schrodinger Equation, Solitons and Organizing Principles for Protein Folding
Molkenthin, Nora; Niemi, Antti J
2010-01-01
We introduce a novel generalization of the discrete nonlinear Schr\\"odinger equation. It supports solitons that describe how proteins fold. As an example we scrutinize the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. Using explicit soliton profiles we construct its carbon backbone with an unprecedented accuracy.
Institute of Scientific and Technical Information of China (English)
P.; K.; A.; Wai
2003-01-01
A nonlinear amplifying loop mirror constructed from erbium-doped fiber is proposed for simultaneous amplification and compression of ultrashort fundamental solitons. Numerical simulations show that, the proposed device performs efficient high-quality amplification and compression of solitons.
Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields
Brauner, Tomas
2016-01-01
The Chiral Soliton Lattice (CSL) is a state with a periodic array of topological solitons that spontaneously breaks parity and translational symmetries. Such a state is known to appear in chiral magnets. We show that CSL also appears as a ground state of quantum chromodynamics at nonzero chemical potential in a magnetic field. By analyzing the fluctuations of the CSL, we furthermore demonstrate that in strong but achievable magnetic fields, charged pions undergo Bose-Einstein condensation. Our results, based on a systematic low-energy effective theory, are model-independent and fully analytic.
Chiral soliton lattice and charged pion condensation in strong magnetic fields
Brauner, Tomáš; Yamamoto, Naoki
2017-04-01
The Chiral Soliton Lattice (CSL) is a state with a periodic array of topological solitons that spontaneously breaks parity and translational symmetries. Such a state is known to appear in chiral magnets. We show that CSL also appears as a ground state of quantum chromodynamics at nonzero chemical potential in a magnetic field. By analyzing the fluctuations of the CSL, we furthermore demonstrate that in strong but achievable magnetic fields, charged pions undergo Bose-Einstein condensation. Our results, based on a systematic low-energy effective theory, are model-independent and fully analytic.
Taylor, J. R.
2005-08-01
1. Optical solitons in fibres: theoretical review A. Hasegawa; 2. Solitons in optical fibres: an experimental account L. F. Mollenauer; 3. All-optical long-distance soliton-based transmission systems K. Smith and L. F. Mollenauer; 4. Nonlinear propagation effects in optical fibres: numerical studies K. J. Blow and N. J. Doran; 5. Soliton-soliton interactions C. Desem and P. L. Chu; 6. Soliton amplification in erbium-doped fibre amplifiers and its application to soliton communication M. Nakazawa; 7. Nonlinear transformation of laser radiation and generation of Raman solitons in optical fibres E. M. Dianov, A. B. Grudinin, A. M. Prokhorov and V. N. Serkin; 8. Generation and compression of femtosecond solitons in optical fibers P. V. Mamyshev; 9. Optical fibre solitons in the presence of higher order dispersion and birefringence C. R. Menyuk and Ping-Kong A. Wai; 10. Dark optical solitons A. M. Weiner; 11. Soliton Raman effects J. R. Taylor; Bibliography; Index.
Mixed dimensional infinite soliton trains for nonlinear Schr\\"odinger equations
Lin, LiRen; Tsai, Tai-Peng
2015-01-01
In this note we construct mixed dimensional infinite soliton trains, which are solutions of nonlinear Schr\\"odinger equations whose asymptotic profiles at time infinity consist of infinitely many solitons of multiple dimensions. For example infinite line-point soliton trains in 2D space, and infinite plane-line-point soliton trains in 3D space. This note extends the works of Le Coz, Li and Tsai [5, 6], where single dimensional trains are considered. In our approach, spatial $L^\\infty$ bounds ...
DEFF Research Database (Denmark)
Zeng, Xianglong; Guo, Hairun; Zhou, Binbin
2012-01-01
In few-cycle soliton generation with large compression factors using cascaded nonlinearities the pulse quality can be improved by engineering quasi-phase-matching structures. The soliton-induced mid-IR optical Cherenkov wave is also enhanced.......In few-cycle soliton generation with large compression factors using cascaded nonlinearities the pulse quality can be improved by engineering quasi-phase-matching structures. The soliton-induced mid-IR optical Cherenkov wave is also enhanced....
Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations.
Piscureanu, M; Manaila-Maximean, D
2000-01-01
We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.
Photorefractive writing and probing of anisotropic linear and non-linear lattices
Allio, Raphaël; Cantillano, Camilo; Morales-Inostroza, Luis; Lopez-Gonzalez, Dany; Etcheverry, Sebastián; Vicencio, Rodrigo A; Armijo, Julien
2014-01-01
We experimentally study the writing of one- and two-dimensional photorefractive lattices and the propagation of linear and nonlinear waves inside them. Using plane waves, we perform a time-resolved study of lattice writing and find good agreement with transient and steady-state photorefractive theory. In particular, the ratio of the drift to diffusion terms is proportional to the lattice period. We then analyze various wave propagation schemes. For focussed linear waves with broad transverse spectrum, we note that both the intensity distributions in real space ("discrete diffraction") and Fourier space ("Brillouin zone spectroscopy") reflect the Bragg planes and band structure. For non-linear waves, we observe modulational instability and time-domain discrete solitons formation. We discuss also the non-ideal effects inherent to the photo-induction technique : anisotropy, parasitic nonlinearity, diffusive term, and non-stationarity.
Obtaining breathers in nonlinear Hamiltonian lattices
Flach, S
1995-01-01
Abstract We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the numerical results. We discuss further applications of the method and results.
Oscillations of the soliton parameters in nonlinear interference phenomena
Energy Technology Data Exchange (ETDEWEB)
Tsoy, Eduard N. [Centre of Excellence for Ultrahigh-bandwidth Devices for Optical Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia)], E-mail: etsoy@physic.uzsci.net; Sterke, C. Martijn de [Centre of Excellence for Ultrahigh-bandwidth Devices for Optical Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia)
2008-03-10
Applying the inverse scattering transform method, we show that a soliton modified by an amplitude or phase filter can evolve into several solitons. The oscillation period upon subsequent propagation follows from the wavenumbers of the emerging solitons and the radiation. Our results clarify spectral variations observed in recent supercontinuum experiments.
Brambila, Danilo
2012-01-01
We have theoretically studied Anderson localization in a 2D+1 nonlinear kicked rotor model. The system shows a very rich dynamical behavior, where the Anderson localization is suppressed and soliton wave-particles undergo a superdiffusive motion.
Breather-to-soliton transformation rules in the hierarchy of nonlinear Schrödinger equations
Chowdury, Amdad; Krolikowski, Wieslaw
2017-06-01
We study the exact first-order soliton and breather solutions of the integrable nonlinear Schrödinger equations hierarchy up to fifth order. We reveal the underlying physical mechanism which transforms a breather into a soliton. Furthermore, we show how the dynamics of the Akhmediev breathers which exist on a constant background as a result of modulation instability, is connected with solitons on a zero background. We also demonstrate that, while a first-order rogue wave can be directly transformed into a soliton, higher-order rogue wave solutions become rational two-soliton solutions with complex collisional structure on a background. Our results will have practical implications in supercontinuum generation, turbulence, and similar other complex nonlinear scenarios.
Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation.
Dmitriev, Sergey V.; Shigenari, Takeshi
2002-06-01
Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.
DEFF Research Database (Denmark)
Bache, Morten; Moses, Jeffrey; Lægsgaard, Jesper;
2007-01-01
We show theoretically that high-quality soliton compression from ~500 fs to ~10 fs is possible in poled silica photonic crystal fibers using cascaded (2):(2) nonlinearities. A moderate group-velocity mismatch optimizes the compression.......We show theoretically that high-quality soliton compression from ~500 fs to ~10 fs is possible in poled silica photonic crystal fibers using cascaded (2):(2) nonlinearities. A moderate group-velocity mismatch optimizes the compression....
Dynamical understanding of loop soliton solution for several nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
Ji-bin LI
2007-01-01
It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.
Nonlinear ultrafast switching based on soliton self-trapping in dual-core photonic crystal fibre
Stajanca, P.; Bugar, I.
2016-11-01
In this paper, we present a systematic numerical study of a novel ultrafast nonlinear switching concept based on soliton self-trapping in dual-core (DC) photonic crystal fibre (PCF). The geometrical parameters of highly-nonlinear (HN) DC microstructure are optimized with regard to desired linear and nonlinear propagation characteristics. The comparable magnitude of fibre coupling length and soliton period is identified as a key condition for presented switching concept. The optimized DC PCF design is subjected to detailed nonlinear numerical study. Complex temporal-spectral-spatial transformations of 100 fs hyperbolic secant pulse at 1550 nm in the DC PCF are studied numerically employing a model based on coupled generalized nonlinear Schrödinger equations solved by a split-step Fourier method. For the optimized DC structure, mutual interplay of solitonic and coupling processes gives rise to nonlinear switching of self-trapped soliton. The output channel (fibre core) for the generated soliton can be controlled via the input pulse energy. For vertical polarization, the optimal soliton switching with extinction ratio contrast of 32.4 dB at 10.75 mm propagation distance is achieved. Even better switching contrast of 34.8 dB can be achieved for horizontal polarization at optimal propagation distance of 10.25 mm. Besides energy-controlled soliton self-trapping switching, the fibre supports also nonlinear polarization switching with soliton switching contrast as high as 37.4 dB. The proposed fibre holds a high application potential allowing efficient ultrafast switching of sub-nanojoule pulses at over-Tb/s data rates requiring only about 1 cm fibre length.
Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Belić, Milivoj [Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Institute of Physics, University of Belgrade, P.O. Box 57, 11001 Belgrade (Serbia)
2014-12-15
We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number, and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.
Dynamics of higher-order solitons in regular and PT-symmetric nonlinear couplers
Driben, R
2012-01-01
Dynamics of symmetric and antisymmetric 2-solitons and 3-solitons is studied in the model of the nonlinear dual-core coupler and its PT-symmetric version. Regions of the convergence of the injected perturbed symmetric and antisymmetric N-solitons into symmetric and asymmetric quasi-solitons are found. In the PT-symmetric system, with the balanced gain and loss acting in the two cores, borders of the stability against the blowup are identified. Notably, in all the cases the stability regions are larger for antisymmetric 2-soliton inputs than for their symmetric counterparts, on the contrary to previously known results for fundamental solitons (N=1). Dynamical regimes (switching) are also studied for the 2-soliton injected into a single core of the coupler. In particular, a region of splitting of the input into a pair of symmetric solitons is found, which is explained as a manifestation of the resonance between the vibrations of the 2-soliton and oscillations of energy between the two cores in the coupler.
Stable scalable control of soliton propagation in broadband nonlinear optical waveguides
Peleg, Avner; Huynh, Toan T
2015-01-01
We develop a method for achieving scalable transmission stabilization and switching of $N$ colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in $N$-sequence transmission is described by a generalized $N$-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of $M$ out of $N$ soliton sequences. Numerical simulations with a system of $N$ coupled nonlinear Schr\\"odinger equations with $2 \\le N \\le 4$ show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear waveguides. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated b...
Solitary heat waves in nonlinear lattices with squared on-site potential
Indian Academy of Sciences (India)
Rovinita Perseus; M M Latha
2013-06-01
A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the properties of heat transfer are examined theoretically. Numerical analysis shows that the propagation of heat is in the form of solitons. Furthermore, a systemized version of tanh method is carried out to extract solutions for the resulting nonlinear equations in the continuum case and the effect of inhomogeneity is studied for different temperatures.
Yang, Jianke
2016-01-01
Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets $(\\lambda, -\\lambda, \\lambda^*, -\\lambda^*)$, similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non-PT-symmetric systems, and it has far-reaching consequences ...
Slowly moving matter-wave gap soliton propagation in weak random nonlinear potential
Institute of Scientific and Technical Information of China (English)
Zhang Ming-Rui; Zhang Yong-Liang; Jiang Xun-Ya; Zi Jian
2008-01-01
We systematically investigate the motion of slowly moving matter-wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitous is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Gross-Pitaevskii equation.
Lattice Theories with Nonlinearly Realized Chiral Symmetry
Chandrasekharan, S; Steffen, F D; Wiese, U J
2003-01-01
We present the lattice formulation of effective Lagrangians in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework both the Wilson term removing unphysical doubler fermions and the fermion mass term do not break chiral symmetry. Our lattice formulation allows us to address non-perturbative questions in effective theories of baryons interacting with pions and in models involving constitutent quarks interacting with pions and gluons. With the presented methods, a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering a complex action problem. This might lead to new insights into the phase diagram of strongly interacting matter at non-zero chemical potential.
Nonlinear Interactions of Dispersion-managed Soliton in OTDM Systems
Institute of Scientific and Technical Information of China (English)
CAI Ju; MAO Yu; LU Hui; ZHANG Li-na; YANG Xiang-lin
2003-01-01
The dispersion-managed soliton (DMS) transmission model of dispersion-managed systems is established,and the intrachannel DMS interactions equation is obtained.The impact of soliton interactions on DMS systems are numerically investigated.Finally,the relationships of the collision length changing with map strength are revealed.
Breatherlike excitations in discrete lattices with noise and nonlinear damping
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri B.; Johansson, Magnus
1997-01-01
We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects...
Bambusi, Dario; Grebert, Benoit
2012-01-01
In this paper we study the long time behavior of a discrete approximation in time and space of the cubic nonlinear Schr\\"odinger equation on the real line. More precisely, we consider a symplectic time splitting integrator applied to a discrete nonlinear Schr\\"odinger equation with additional Dirichlet boundary conditions on a large interval. We give conditions ensuring the existence of a numerical soliton which is close in energy norm to the continuous soliton. Such result is valid under a CFL condition between the time and space stepsizes. Furthermore we prove that if the initial datum is symmetric and close to the continuous soliton, then the associated numerical solution remains close to the orbit of the continuous soliton for very long times.
Energy Technology Data Exchange (ETDEWEB)
Kakad, Amar [Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto 611-0011 (Japan); Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410-218 (India); Omura, Yoshiharu [Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto 611-0011 (Japan); Kakad, Bharati [Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410-218 (India)
2013-06-15
We perform one-dimensional fluid simulation of ion acoustic (IA) solitons propagating parallel to the magnetic field in electron-ion plasmas by assuming a large system length. To model the initial density perturbations (IDP), we employ a KdV soliton type solution. Our simulation demonstrates that the generation mechanism of IA solitons depends on the wavelength of the IDP. The short wavelength IDP evolve into two oppositely propagating identical IA solitons, whereas the long wavelength IDP develop into two indistinguishable chains of multiple IA solitons through a wave breaking process. The wave breaking occurs close to the time when electrostatic energy exceeds half of the kinetic energy of the electron fluid. The wave breaking amplitude and time of its initiation are found to be dependent on characteristics of the IDP. The strength of the IDP controls the number of IA solitons in the solitary chains. The speed, width, and amplitude of IA solitons estimated during their stable propagation in the simulation are in good agreement with the nonlinear fluid theory. This fluid simulation is the first to confirm the validity of the general nonlinear fluid theory, which is widely used in the study of solitary waves in laboratory and space plasmas.
Periodic modulations controlling Kuznetsov–Ma soliton formation in nonlinear Schrödinger equations
Energy Technology Data Exchange (ETDEWEB)
Tiofack, C.G.L., E-mail: glatchio@yahoo.fr [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); Coulibaly, S.; Taki, M. [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); De Bièvre, S.; Dujardin, G. [Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, F-59000 Lille (France); Équipe-Projet Mephysto, INRIA Lille-Nord Europe (France)
2017-06-28
We analyze the exact Kuznetsov–Ma soliton solution of the one-dimensional nonlinear Schrödinger equation in the presence of periodic modulations satisfying an integrability condition. We show that, in contrast to the case without modulation, the Kuznetsov–Ma soliton develops multiple compression points whose number, shape and position are controlled both by the intensity of the modulation and by its frequency. In addition, when this modulation frequency is a rational multiple of the natural frequency of the Kuznetsov–Ma soliton, a scenario similar to a nonlinear resonance is obtained: in this case the spatial oscillations of the Kuznetsov–Ma soliton's intensity are periodic. When the ratio of the two frequencies is irrational, the soliton's intensity is a quasiperiodic function. A striking and important result of our analysis is the possibility to suppress any component of the output spectrum of the Kuznetsov–Ma soliton by a judicious choice of the amplitude and frequency of the modulation. - Highlights: • Exact Kuznetsov–Ma soliton solution in presence of periodic coefficients is obtained. • The multiple compression points of the solution are studied. • The quasi-periodicity of the solution is discussed. • The possibility to suppress any component of the spectrum is analyzed.
On the Link between Umbilic Geodesics and Soliton Solutions of Nonlinear PDEs
1995-01-01
In this paper we describe a new class of soliton solutions, called umbilic solitons, for certain nonlinear integrable PDES. These umbilic solitons have the property that as the space variable x tends to infinity, the solution tends to a periodic wave, and as x tends to minus infinity, it tends to a phase shifted wave of the same shape. The equations admitting solutions in this new class include the Dym equation and equations in its hierarchy. The methods used to find and analyse these solutio...
Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation
Directory of Open Access Journals (Sweden)
Hai-Feng Zhang
2013-01-01
Full Text Available A generalized nonlinear Schrödinger equation, which describes the propagation of the femtosecond pulse in single mode optical silica fiber, is analytically investigated. By virtue of the Darboux transformation method, some new soliton solutions are generated: the bright one-soliton solution on the zero background, the dark one-soliton solution on the continuous wave background, the Akhmediev breather which delineates the modulation instability process, and the breather evolving periodically along the straight line with a certain angle of x-axis and t-axis. Those results might be useful in the study of the femtosecond pulse in single mode optical silica fiber.
A Lower Bound on the per Soliton Capacity of the Nonlinear Optical Fibre Channel
Shevchenko, Nikita A; Derevyanko, Stanislav A; Alvarado, Alex; Bayvel, Polina; Turitsyn, Sergei K
2015-01-01
A closed-form expression for a lower bound on the per soliton capacity of the nonlinear optical fibre channel in the presence of (optical) amplifier spontaneous emission (ASE) noise is derived. This bound is based on a non-Gaussian conditional probability density function for the soliton amplitude jitter induced by the ASE noise and is proven to grow logarithmically as the signal-to-noise ratio increases.
Explicit Soliton and Periodic Solutions to Three-Wave System with Quadratic and Cubic Nonlinearities
Institute of Scientific and Technical Information of China (English)
LIN Ji; ZHAO Li-Na; LI Hua-Mei
2011-01-01
Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing x(2)(quadratic) and x(3) (cubic) nonlinearities and birefringence.This system shares some of the nice properties of soliton system.On the phase-locked condition, we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.
Indian Academy of Sciences (India)
P A Subha; C P Jisha; V C Kuriakose
2007-08-01
The nonlinear Schrödinger equation which governs the dynamics of two-dimensional spatial solitons in Kerr media with periodically varying diffraction and nonlinearity has been analyzed in this paper using variational approach and numerical studies. Analytical expressions for soliton parameters have been derived using variational analysis. Variational equations and partial differential equation have been simulated numerically. Analytical and numerical studies have shown that nonlinearity management and diffraction management stabilize the pulse against decay or collapse providing undisturbed propagation even for larger energies of the incident beam.
Zabusky, Norman J
2005-03-01
This paper is mostly a history of the early years of nonlinear and computational physics and mathematics. I trace how the counterintuitive result of near-recurrence to an initial condition in the first scientific digital computer simulation led to the discovery of the soliton in a later computer simulation. The 1955 report by Fermi, Pasta, and Ulam (FPU) described their simulation of a one-dimensional nonlinear lattice which did not show energy equipartition. The 1965 paper by Zabusky and Kruskalshowed that the Korteweg-de Vries (KdV) nonlinear partial differential equation, a long wavelength model of the alpha-lattice (or cubic nonlinearity), derived by Kruskal, gave quantitatively the same results obtained by FPU. In 1967, Zabusky and Deem showed that a localized short wavelength initial excitation (then called an "optical" and now a "zone-boundary mode" excitation ) of the alpha-lattice revealed "n-curve" coherent states. If the initial amplitude was sufficiently large energy equipartition followed in a short time. The work of Kruskal and Miura (KM), Gardner and Greene (GG), and myself led to the appreciation of the infinity of denumerable invariants (conservation laws) for Hamiltonian systems and to a procedure by GGKM in 1967 for solving KdV exactly. The nonlinear science field exponentiated in diversity of linkages (as described in Appendix A). Included were pure and applied mathematics and all branches of basic and applied physics, including the first nonhydrodynamic application to optical solitons, as described in a brief essay (Appendix B) by Hasegawa. The growth was also manifest in the number of meetings held and institutes founded, as described briefly in Appendix D. Physicists and mathematicians in Japan, USA, and USSR (in the latter two, people associated with plasma physics) contributed to the diversification of the nonlinear paradigm which continues worldwide to the present. The last part of the paper (and Appendix C) discuss visiometrics: the
Stability of two-dimensional spatial solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Skupin, S.; Bang, Ole; Edmundson, D.;
2006-01-01
We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating...
E Heebner, John; Boyd, Robert W; Park, Q-Han
2002-03-01
We describe an optical transmission line that consists of an array of wavelength-scale optical disk resonators coupled to an optical waveguide. Such a structure leads to exotic optical characteristics, including ultraslow group velocities of propagation, enhanced optical nonlinearities, and large dispersion with a controllable magnitude and sign. This device supports soliton propagation, which can be described by a generalized nonlinear Schrodinger equation.
Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Teixeira, Rafael M.P.; Cardoso, Wesley B., E-mail: wesleybcardoso@gmail.com
2016-08-12
In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schrödinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enables us the possibility of controlling the scattering of solitons as well as the lifetime of bound states. - Highlights: • We study the interaction of Gaussian solitons in a system with log-law nonlinearity. • The model is described by the coupled logarithmic nonlinear Schrödinger equations. • We observe a fractal-scattering phenomenon of the solitons.
Crosta, M.
2011-12-05
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Rajan, M. S. Mani
2016-08-01
In this manuscript, the ultrashort soliton pulse propagation through nonlinear tunneling in cubic quintic media is investigated. The effect of chirping on propagation characteristics of the soliton pulse is analytically investigated using similarity transformation. In particular, we investigate the propagation dynamics of ultrashort soliton pulse through dispersion barrier for both chirp and chirp-free soliton. By investigating the obtained soliton solution, we found that chirping has strong influence on soliton dynamics such as pulse compression with amplification. These two important dynamics of chirped soliton in cubic quintic media open new possibilities to improve the solitonic communication system. Moreover, we surprisingly observe that a dispersion well is formed for the chirped case whereas a barrier is formed for the chirp-free case, which has certain applications in the construction of logic gate devices to achieve ultrafast switching.
Chetverikov, A. P.; Ebeling, W.; Velarde, M. G.
2016-09-01
We present computational evidence of the possibility of fast, supersonic or subsonic, nearly loss-free ballistic-like transport of electrons bound to lattice solitons (a form of electron surfing on acoustic waves) along crystallographic axes in two-dimensional anharmonic crystal lattices. First we study the structural changes a soliton creates in the lattice and the time lapse of recovery of the lattice. Then we study the behavior of one electron in the polarization field of one and two solitons with crossing pathways with suitably monitored delay. We show how an electron surfing on a lattice soliton may switch to surf on the second soliton and hence changing accordingly the direction of its path. Finally we discuss the possibility to control the way an excess electron proceeds from a source at a border of the lattice to a selected drain at another border by following appropriate straight pathways on crystallographic axes.
Neutron scattering study of the field-induced soliton lattice in CuGeO_{3}
DEFF Research Database (Denmark)
Rønnow, H.M.; Enderle, M.; McMorrow, D.F.
2000-01-01
CuGeO3 undergoes a transition from a spin-Peierls phase to an incommensurate phase at a critical field of H-c approximate to 12.5 T. In the high-field phase a lattice of solitons forms, with both structural and magnetic components, and these have been studied using neutron scattering techniques....... Our results provide direct evidence for a long-ranged magnetic soliton structure which has both staggered and uniform magnetizations with amplitudes that are broadly in accord with theoretical estimates. The magnetic soliton width Gamma(m) and the field dependence of the incommensurability delta k...
Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Karpman, V.I.; Juul Rasmussen, J.; Shagalov, A.G.
2001-01-01
The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrodinger equation is studied. Regular solitons exist due to a balance between the nonlinear terms and (linear) third-order dispersion; they are not important at small alpha (3) (alpha (3) is the coefficient...
Controlled soliton formation in tailored Bessel photonic lattices.
Diebel, Falko; Boguslawski, Martin; Dadalyan, Tigran; Drampyan, Rafael; Denz, Cornelia
2016-06-13
Azimuthally modulated higher order rotationally symmetric Bessel-like optical patterns were generated by coherent superposition of two co-propagating Bessel beams - either in or out of phase. By changing the distance between the beam centers, a whole variety of transition states can be realized. As one prominent example, a 4-fold symmetry quadrupole-like photonic structure was optically inducted in an SBN crystal and nonlinear beam propagation in such a photonic wave-guiding structure is investigated in both self-focusing and self-defocusing regimes. The proposed device serves as an all-optical 2d 1 × 4 photonic interconnect.
Trapping of two-component matter-wave solitons by mismatched optical lattices
Energy Technology Data Exchange (ETDEWEB)
Shi, Z.; Law, K.J.H. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States)], E-mail: kevrekid@gmail.com; Malomed, B.A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
2008-05-26
We consider a one-dimensional model of a two-component Bose-Einstein condensate in the presence of periodic external potentials of opposite signs, acting on the two species. The interaction between the species is attractive, while intra-species interactions may be attractive too [the system of the bright-bright (BB) type], or of opposite signs in the two components [the gap-bright (GB) type]. We identify the existence and stability domains for soliton complexes of the BB and GB types. The evolution of unstable solitons leads to the establishment of oscillatory states. The increase of the strength of the nonlinear attraction between the species results in symbiotic stabilization of the complexes, despite the fact that one component is centered around a local maximum of the respective periodic potential.
A Unified and Explicit Construction of N-Soliton Solutions for the Nonlinear Schrfdinger Equation
Institute of Scientific and Technical Information of China (English)
FAN En-Gui
2001-01-01
An explicit N-fold Darboux transformation with multiparameters for nonlinear Schrodinger equation is constructed with the help of its Lax pairs and a reduction technique. According to this Darboux transformation, the solutions of the nonlinear Schrfdinger equation are reduced to solving a linear algebraic system, from which a unified and explicit formulation of N-soliton solutions with multiparameters for the nonlinear Schrfdinger equation is given.``
Solitons in a chain of PT-invariant dimers
Suchkov, Sergey V; Dmitriev, Sergey V; Kivshar, Yuri S
2011-01-01
Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrodinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anti-continuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear PT-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability...
Stable scalable control of soliton propagation in broadband nonlinear optical waveguides
Peleg, Avner; Nguyen, Quan M.; Huynh, Toan T.
2017-02-01
We develop a method for achieving scalable transmission stabilization and switching of N colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in N-sequence transmission is described by a generalized N-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of M out of N soliton sequences. Numerical simulations for single-waveguide transmission with a system of N coupled nonlinear Schrödinger equations with 2 ≤ N ≤ 4 show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.
Travelling and standing envelope solitons in discrete non-linear cyclic structures
Grolet, Aurelien; Hoffmann, Norbert; Thouverez, Fabrice; Schwingshackl, Christoph
2016-12-01
Envelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery.
Some Remarks on Similarity and Soliton Solutions of Nonlinear Klein-Gordon Equation
Tajiri, Masayoshi
1984-11-01
The three-dimensional nonlinear Klein-Gordon [, Higgs field and Yang-Milles] (3D-KG [, H and YM]) equation is first reduced to the 2D nonlinear Schrödinger (2D-NLS) and 2D-KG [, H and YM] equations, and secondly to the 1D-NLS and 1D-KG [, H and YM] equations by similarity transformations. It is shown that similar type soliton solutions of the 3D-KG, H and YM equations, which have singularity on a plane in (x, y, z, t) space, are obtained by substituting the soliton solutions of the 1D-NLS or 1D-KG (or H) equation into the similarity transformations. The soliton solutions of the YM equation are also investigated.
Wave train generation of solitons in systems with higher-order nonlinearities.
Mohamadou, Alidou; LatchioTiofack, C G; Kofané, Timoléon C
2010-07-01
Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain. Experimental values are used for the numerical simulations and the input plane wave leads to the development of pulse trains, depending upon the sign of the septic nonlinearity.
Goos-Hänchen shifts of Helmholtz solitons at nonlocal nonlinear interfaces
Zhiwei, Shi; Jing, Xue; Jilong, Chen; Yang, Li; Huagang, Li
2015-02-01
We address the nonlinear Goos-Hänchen shift of Helmholtz solitons at a nonlocal nonlinear interface between a Kerr medium and a nonlocal nonlinear medium. Based on the framework of the Helmholtz theory, we have demonstrated that the Goos-Hänchen shift depends on the angle of the incidence, the linear and nonlinear refractive index mismatch at the interface, the nonparaxial parameter and the degree of nonlocality. Interestingly, internal and external refraction can be introduced when the nonlinear refractive index mismatch is greater than a threshold value. The total reflection will occur when the degree of nonlocality exceeds a value.
Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity.
Merhasin, Ilya M; Gisin, Boris V; Driben, Rodislav; Malomed, Boris A
2005-01-01
We present a model combining a periodic array of rectangular potential wells [the Kronig-Penney (KP) potential] and the cubic-quintic (CQ) nonlinearity. A plethora of soliton states is found in the system: fundamental single-humped solitons, symmetric and antisymmetric double-humped ones, three-peak solitons with and without the phase shift pi between the peaks, etc. If the potential profile is shallow, the solitons belong to the semi-infinite gap beneath the band structure of the linear KP model, while finite gaps between the Bloch bands remain empty. However, in contrast with the situation known in the model combining a periodic potential and the self-focusing Kerr nonlinearity, the solitons fill only a finite zone near the top of the semi-infinite gap, which is a consequence of the saturable character of the CQ nonlinearity. If the potential structure is much deeper, then fundamental and double (both symmetric and antisymmetric) solitons with a flat-top shape are found in the finite gaps. Computation of stability eigenvalues for small perturbations and direct simulations show that all the solitons are stable. In the shallow KP potential, the soliton characteristics, in the form of the integral power Q (or width w) versus the propagation constant k, reveal strong bistability, with two and, sometimes, four different solutions found for a given k (the bistability disappears with the increase of the depth of the potential). Disobeying the Vakhitov-Kolokolov criterion, the solution branches with both dQ/dk > 0 and dQ/dk < 0 are stable. The curve Q(k) corresponding to each particular type of the solution (with a given number of local peaks and definite symmetry) ends at a finite maximum value of Q (breathers are found past the end points). The increase of the integral power gives rise to additional peaks in the soliton's shape, each corresponding to a subpulse trapped in a local channel of the KP structure (a beam-splitting property). It is plausible that these
Bragg solitons in systems with separated nonuniform Bragg grating and nonlinearity
Ahmed, Tanvir; Atai, Javid
2017-09-01
The existence and stability of quiescent Bragg grating solitons are systematically investigated in a dual-core fiber, where one of the cores is uniform and has Kerr nonlinearity while the other one is linear and incorporates a Bragg grating with dispersive reflectivity. Three spectral gaps are identified in the system, in which both lower and upper band gaps overlap with one branch of the continuous spectrum; therefore, these are not genuine band gaps. However, the central band gap is a genuine band gap. Soliton solutions are found in the lower and upper gaps only. It is found that in certain parameter ranges, the solitons develop side lobes. To analyze the side lobes, we have derived exact analytical expressions for the tails of solitons that are in excellent agreement with the numerical solutions. We have analyzed the stability of solitons in the system by means of systematic numerical simulations. We have found vast stable regions in the upper and lower gaps. The effect and interplay of dispersive reflectivity, the group velocity difference, and the grating-induced coupling on the stability of solitons are investigated. A key finding is that a stronger grating-induced coupling coefficient counteracts the stabilization effect of dispersive reflectivity.
Institute of Scientific and Technical Information of China (English)
FAN Eh-Gui
2001-01-01
An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrodinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transformation for well-known Gerdjikov-Ivanov equation is further obtained, from which a general form of N-soliton solutions for Gerdjikov-Ivanov equation is given.``
The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber
Directory of Open Access Journals (Sweden)
Feng-Tao He
2013-01-01
Full Text Available We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton’s dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1 if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton’s width increases, while its amplitude and wave velocity reduce. (2 If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton’s width increases, while its amplitude and the wave velocity reduce.
Soliton-potential interaction in the Nonlinear Klein-Gordon Model
Saadatmand, Danial
2011-01-01
Interaction of solitons with external potentials in nonlinear Klein-Gordon field theory is investigated using an improved model. Presented model is constructed with a better approximation for adding the potential to the lagrangian through the metric of background space-time. The results of the model are compared with the another model and the differences are discussed.
Leblond, Hervé; Malomed, Boris A; Mihalache, Dumitru
2005-03-01
We consider basic types of two-dimensional (2D) vortex solitons in a three-wave model combining quadratic chi((2)) and self-defocusing cubic chi((3))(-) nonlinearities. The system involves two fundamental-frequency (FF) waves with orthogonal polarizations and a single second-harmonic (SH) one. The model makes it possible to introduce a 2D soliton, with hidden vorticity (HV). Its vorticities in the two FF components are S(1,2) = +/-1 , whereas the SH carries no vorticity, S(3) = 0 . We also consider an ordinary compound vortex, with 2S(1) = 2S(2) = S(3) = 2 . Without the chi((3))(-) terms, the HV soliton and the ordinary vortex are moderately unstable. Within the propagation distance z approximately 15 diffraction lengths, Z(diffr), the former one turns itself into a usual zero-vorticity (ZV) soliton, while the latter splits into three ZV solitons (the splinters form a necklace pattern, with its own intrinsic dynamics). To gain analytical insight into the azimuthal instability of the HV solitons, we also consider its one-dimensional counterpart, viz., the modulational instability (MI) of a one-dimensional CW (continuous-wave) state with "hidden momentum," i.e., opposite wave numbers in its two components, concluding that such wave numbers may partly suppress the MI. As concerns analytical results, we also find exact solutions for spreading localized vortices in the 2D linear model; in terms of quantum mechanics, these are coherent states with angular momentum (we need these solutions to accurately define the diffraction length of the true solitons). The addition of the chi((3))(-) interaction strongly stabilizes both the HV solitons and the ordinary vortices, helping them to persist over z up to 50 Z(diffr). In terms of the possible experiment, they are completely stable objects. After very long propagation, the HV soliton splits into two ZV solitons, while the vortex with S(3) = 2S(1,2) = 2 splits into a set of three or four ZV solitons.
Numerical Studies of Localized Vibrating Structures in Nonlinear Lattices
1991-03-01
lattice, from Denardo [19901. 11 strings which supported adjacent elements , and was assumed to be approximately linear. For our purposes, we will assume a...City, State, and ZIP Code) 10 SOURCE OF FUNDING NUMBERS PROGRAM PROJECT TASK WORK UNIT ELEMENT NO NO NO ACCESSION NO 11 TITLE (Include Security...art in cosmology , particle physics, condensed matter physics, and hydrodynamics, to name but a few. Most of the soliton work performed to date has
Singular and non-topological soliton solutions for nonlinear fractional differential equations
Institute of Scientific and Technical Information of China (English)
Ozkan Guner
2015-01-01
In this article, the fractional derivatives are described in the modified Riemann–Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations (FDEs) based on a fractional complex transform and apply it to solve nonlinear space–time fractional equations. As a result, the non-topological as well as the singular soliton solutions are obtained. This method can be suitable and more powerful for solving other kinds of nonlinear fractional FDEs arising in mathematical physics.
Directory of Open Access Journals (Sweden)
Juan Belmonte-Beitia
2008-01-01
Full Text Available We give a proof of the existence of stationary bright soliton solutions of the cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity. By using bifurcation theory, we prove that the norm of the positive solution goes to zero as the parameter λ, called chemical potential in the Bose-Einstein condensates' literature, tends to zero. Moreover, we solve the time-dependent cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearities by using a numerical method.
Institute of Scientific and Technical Information of China (English)
Chen Xiong-Wen; Lin Xu-Sheng; Lan Sheng
2005-01-01
We investigate by numerical simulation the compression of subpicosecond pulses in two-dimensional nonlinear photonic crystal (PC) waveguides. The compression originates from the generation of high-order optical solitons through the interplay of the huge group-velocity dispersion and the enhanced self-phase modulation in nonlinear PC waveguides.Both the formation of Bragg grating solitons and gap solitons can lead to efficient pulse compression. The compression factors under different excitation power densities and the optimum length for subpicosecond pulse compression have been determined. As a compressor, the total length of the nonlinear PC waveguide is only ten micrometres and therefore can be easily incorporated into PC integrated circuits.
Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons
Midya, Bikashkali; Konotop, Vladimir V.
2017-07-01
We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e., the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of the carried eigenmode when the surface impedance encircles the exceptional point. In its turn, the change of the effective nonlinearity ensures the existence of dark (bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the core. The existence of an exceptional point can also result in anomalous enhancement of the effective nonlinearity. In terms of practical applications, the nonlinearity of the reported waveguide can be manipulated by controlling the properties of the absorbing cladding.
Integrable Nonlinear Schrödinger System on a Triangular-Lattice Ribbon
Vakhnenko, Oleksiy O.
2015-01-01
An integrable nonlinear Schrödinger system on a triangular-lattice ribbon, whose geometric configuration is similar to that of (1,1) armchair boron nanotube, is studied in detail. The system Hamiltonian formulation is shown to underline an essentially nontrivial Poisson structure associated with four basic field variables appearing as nearly amplitudes of the probability to find the lattice sites being excited and with two concomitant field variables maintaining the finite background. The coupling parameters of the system are allowed to be complex-valued ones thus permitting to model external magnetic fluxes threading the elementary plackets of a lattice in terms of Peierls phases. An alternative version of zero-curvature representation given in terms of 2 × 2 auxiliary spectral and evolution matrices is proved to support the constructive integrability of the system by means of Darboux-Bäcklund dressing method. In the framework of Darboux approach the one-soliton solution is found explicitly and analyzed with special attention to the principal differences between the bare and physical soliton parameters.
DEFF Research Database (Denmark)
Oster, Michael; Gaididei, Yuri B.; Johansson, Magnus
2004-01-01
We study the continuum limit of a nonlinear Schrodinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose-Einstein condensates. The resulting continuum nonlinear Schrodinger-type equation includes both nonlocal and nonlinear...
Cusp solitons and cusp-like singular solutions for nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Qiao Zhijun [Department of Mathematics, University of Texas Pan-American, 1201 West University Drive, Edinburg, TX 78539 (United States) and Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: qiao@utpa.edu; Qiao, Xin Brian [Memorial High School, 101E Hackberry, McAllen TX 78501 (United States)
2005-07-01
This paper gives two new families of nonlinear partial differential equations (PDEs). One has cusp soliton solution while the other possesses the cusp-like singular traveling wave solution. A typical integrable system: Harry-Dym (HD) equation is able to be contained in both families and has cusp soliton solution as well as cusp-like singular traveling wave solution. We prove that the cusp solution of the HD equation is not stable and the cusp-like solution is not included in the parametric solutions of the HD equati0008.
Kong, Lingjie; Xiao, Xiaosheng; Yang, Changxi
2011-09-12
We numerically studied the polarization dynamics in dissipative soliton lasers mode-locked by nonlinear polarization rotation (NPR). It was found that the polarization states of the intracavity dissipative soliton vary with time across the pulse. Depending on output coupling ratios, the polarization states of the pulse peak before the polarizer can be either nearly circular or nearly linear polarizations. The polarization dependent component in NPR is found to play a role of spectral filter under high and medium output coupling. However, NPR may work as a weak optical limiter under low output coupling, when additional spectral filtering is necessary to maintain steady mode-locking state.
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian that nonloc......We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian...
Soliton clusters in three-dimensional media with competing cubic and quintic nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Mihalache, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Mazilu, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Crasovan, L-C [ICFO-Institut de Ciencies Fotoniques and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, ES 8034 Barcelona (Spain); Malomed, B A [Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Lederer, F [Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, D-07743, Jena (Germany); Torner, L [ICFO-Institut de Ciencies Fotoniques and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, ES 8034 Barcelona (Spain)
2004-05-01
We introduce a class of robust soliton clusters composed of N fundamental solitons in three-dimensional media combining the self-focusing cubic and self-defocusing quintic nonlinearities. The angular momentum is lent to the initial cluster through staircase or continuous ramp-like phase distribution. Formation of these clusters is predicted analytically, by calculating an effective interaction Hamiltonian H{sub int}. If a minimum of H{sub int} is found, direct three-dimensional simulations demonstrate that, when the initial pattern is close to the predicted equilibrium size, a very robust rotating cluster does indeed exist, featuring persistent oscillations around the equilibrium configuration (clusters composed of N = 4,5, and 6 fundamental solitons are investigated in detail). If a strong random noise is added to the initial configuration, the cluster eventually develops instability, either splitting into several fundamental solitons or fusing into a nearly axisymmetric vortex torus. These outcomes match the stability or instability of the three-dimensional vortex solitons with the same energy and spin; in particular, the number of the fragments in the case of the break-up is different from the number of solitons in the original cluster, being instead determined by the dominant mode of the azimuthal instability of the corresponding vortex soliton. The initial form of the phase distribution is important too: under the action of the noise, the cluster with the built-in staircase-like phase profile features azimuthal instability, while the one with the continuous distribution fuses into a vortex torus.
Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K
2017-02-01
We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.
Fast Inverse Nonlinear Fourier Transform For Generating Multi-Solitons In Optical Fiber
Wahls, Sander
2015-01-01
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only $\\mathcal{O}(D\\log^{2}D)$ floating point operations to compute $D$ samples of a multi-soliton. To the best of our knowledge, this is the first algorithm for this problem with $\\log^{2}$-linear complexity. The paper also includes a many samples analysis of the generated nonlinear Fourier spectra.
DEFF Research Database (Denmark)
Bache, Morten; Lægsgaard, Jesper; Bang, Ole;
2007-01-01
We investigate the possibility of using poled silica photonic crystal fibers for self-defocusing soliton compression with cascaded quadratic nonlinearities. Such a configuration has promise due to the desirable possibility of reducing the group-velocity mismatch. However, this unfortunately leads...... nonlinearity, and show that compression of nJ pulses to few-cycle duration is possible in such a fiber. A small amount of group-velocity mismatch optimizes the compression.......We investigate the possibility of using poled silica photonic crystal fibers for self-defocusing soliton compression with cascaded quadratic nonlinearities. Such a configuration has promise due to the desirable possibility of reducing the group-velocity mismatch. However, this unfortunately leads...
Guo, Bang-Xing; Gao, Zhan-Jie; Lin, Ji
2016-12-01
The consistent tanh expansion (CTE) method is applied to the (2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution, and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlevé truncated expansion method. And we investigate interactive properties of solitons and periodic waves. Supported by the National Natural Science Foundation of Zhejiang Province under Grant No. LZ15A050001 and the National Natural Science Foundation of China under Grant No. 11675164
Small Amplitude Solitons in the Higher-Order Nonlinear Schr(o)dinger Equation in an Optical Fibre
Institute of Scientific and Technical Information of China (English)
王凤姣; 唐翌
2003-01-01
By taking advantage of the approximate approach of small amplitude soliton, we study the higher-order nonlinear Schrodinger equation in an optical fibre. Our results show that the bright and dark solitons of small amplitude can appear on the background of a continuous wave in normal dispersion regime or in anomalous dispersion regime simultaneously due to the higher-order effects. Interesting connection between the higher-order nonlinear Schrodinger equation and the Korteweg-de Vries equation is also demonstrated.
Soliton dynamics in the multiphoton plasma regime
Husko, Chad A; Colman, Pierre; Zheng, Jiangjun; De Rossi, Alfredo; Wong, Chee Wei; 10.1038/srep01100
2013-01-01
Solitary waves have consistently captured the imagination of scientists, ranging from fundamental breakthroughs in spectroscopy and metrology enabled by supercontinuum light, to gap solitons for dispersionless slow-light, and discrete spatial solitons in lattices, amongst others. Recent progress in strong-field atomic physics include impressive demonstrations of attosecond pulses and high-harmonic generation via photoionization of free-electrons in gases at extreme intensities of 1014 Wcm2. Here we report the first phase-resolved observations of femtosecond optical solitons in a semiconductor microchip, with multiphoton ionization at picojoule energies and 1010 Wcm2 intensities. The dramatic nonlinearity leads to picojoule observations of free-electron-induced blue-shift at 1016 cm3 carrier densities and self-chirped femtosecond soliton acceleration. Furthermore, we evidence the time-gated dynamics of soliton splitting on-chip, and the suppression of soliton recurrence due to fast free-electron dynamics. Thes...
Nonautonomous Solitons in the （3＋1）-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium
Institute of Scientific and Technical Information of China (English)
刘翠云; 戴朝卿
2012-01-01
We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Sehr6dinger equation in the （3＋ 1 ）-dimensionM inhomogeneous cubic-quintic nonlinear medium. The gain parameter has no effects on the motion of the soliton＇s phase or their velocities, and it affects just the evolution of their peaks. As two examples, we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system. Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly, but also broadens their width.
Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles.
Noskov, Roman; Belov, Pavel; Kivshar, Yuri
2012-01-01
The study of metal nanoparticles plays a central role in the emerging novel technologies employing optics beyond the diffraction limit. Combining strong surface plasmon resonances, high intrinsic nonlinearities and deeply subwavelength scales, arrays of metal nanoparticles offer a unique playground to develop novel concepts for light manipulation at the nanoscale. Here we suggest a novel principle to control localized optical energy in chains of nonlinear subwavelength metal nanoparticles based on the fundamental nonlinear phenomenon of modulation instability. In particular, we demonstrate that modulation instability can lead to the formation of long-lived standing and moving nonlinear localized modes of several distinct types such as bright and dark solitons, oscillons, and domain walls. We analyze the properties of these nonlinear localized modes and reveal different scenarios of their dynamics including transformation of one type of mode to another. We believe this work paves a way towards the development of nonlinear nanophotonics circuitry.
Logarithmic divergent thermal conductivity in two-dimensional nonlinear lattices.
Wang, Lei; Hu, Bambi; Li, Baowen
2012-10-01
Heat conduction in three two-dimensional (2D) momentum-conserving nonlinear lattices are numerically calculated via both nonequilibrium heat-bath and equilibrium Green-Kubo algorithms. It is expected by mainstream theories that heat conduction in such 2D lattices is divergent and the thermal conductivity κ increases with lattice length N logarithmically. Our simulations for the purely quartic lattice firmly confirm it. However, very robust finite-size effects are observed in the calculations for the other two lattices, which well explain some existing studies and imply the extreme difficulties in observing their true asymptotic behaviors with affordable computation resources.
Yang, Yunqing; Malomed, Boris A
2015-01-01
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel (LPD) equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
An Envelope Soliton in a Nonlinear Chain with the Power-Law Dependence of Long-Range Interaction
Institute of Scientific and Technical Information of China (English)
王登龙; 颜晓红; 唐翌
2003-01-01
We study the Fermi-Pasta-Ulam lattice model in the presence ora power-law dependence of long-range interaction by virtue of the method of multiple scales. Our results show that an envelope soliton still appears, but it is of different property for the group velocity compared with that of the soliton in the model when long-range interaction is absent.
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
Influence of group—velocity mismatch on soliton switching in a nonlinear fibre coupler
Institute of Scientific and Technical Information of China (English)
LiHong; HuangDe-Xiu; WangDong-Ning
2003-01-01
In this work, the influence of group-velocity mismatch on soliton self-routing pulse switching in a nonlinear fibre coupler is discussed in detail by the use of both variational approach and numerical simulation. The results obtained show that the group-velocity mismatch leads to the relative displacement between the two orthogonal polarization modes, increase of the critical power, and reduction of the elimination-light ratio. For sub-ps pulse, the influence cannot be neglected.
Influence of group-velocity mismatch on soliton switching in a nonlinear fibre coupler
Institute of Scientific and Technical Information of China (English)
李宏; 黄德修; 王东宁
2003-01-01
In this work, the influence of group-velocity mismatch on soliton self-routing pulse switching in a nonlinear fibrecoupler is discussed in detail by the use of both variational approach and numerical simulation. The results obtainedshow that the group-velocity mismatch leads to the relative displacement between the two orthogonal polarizationmodes, increase of the critical power, and reduction of the elimination-light ratio. For sub-ps pulse, the influence cannot be neglected.
Singular solitons and other solutions to a couple of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
Mustafa Inc; Esma Uluta(s); Anjan Biswas
2013-01-01
This paper addresses the extended (G′/G)-expansion method and applies it to a couple of nonlinear wave equations.These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation.This extended method reveals several solutions to these equations.Additionally,the singular soliton solutions are revealed,for these two equations,with the aid of the ansatz method.
光学格点中玻色-爱因斯坦凝聚的自旋孤子%Solitons of spinor Bose-Einstein condensates in an optical lattice
Institute of Scientific and Technical Information of China (English)
谢元栋
2007-01-01
An improved nonlinear equation different from usual and an improved soliton solution of spinor Bose-Einstein condensates (BES) in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The width,peak and energy of soliton are also found.%得到了一个有关光学格点中的玻色-爱因斯坦凝聚的改进的非线性薛定谔方程,并且通过仔细考察自旋概率幅方程的高阶非线性项,求得了一个改进孤子解.并求出了孤子的宽度、峰值和能量.
Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity
Zeng, Jianhua
2012-01-01
It has been recently demonstrated that self-defocusing (SDF) media with the cubic nonlinearity, whose local coefficient grows from the center to periphery fast enough, support stable bright solitons, without the use of any linear potential. Our objective is to test the genericity of this mechanism for other nonlinearities, by applying it to one- and two-dimensional (1D and 2D) quintic SDF media. The models may be implemented in optics (in particular, in colloidal suspensions of nanoparticles), and the 1D model may be applied to the description of the Tonks-Girardeau gas of ultracold bosons. In 1D, the nonlinearity-modulation function is taken as $% g_{0}+\\sinh ^{2}(\\beta x) $. This model admits a subfamily of exact solutions for fundamental solitons. Generic \\ soliton solutions are constructed in a numerical form, and also by means of the Thomas-Fermi and variational approximations (TFA and VA). In particular, a new ansatz for the VA is proposed, in the form of "raised $\\mathrm{sech}$", which provides for an ...
Spatiotemporal optical solitons
Energy Technology Data Exchange (ETDEWEB)
Malomed, Boris A [Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Mihalache, Dumitru [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Wise, Frank [Department of Applied Physics, 212 Clark Hall, Cornell University, Ithaca, NY 14853 (United States); Torner, Lluis [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, Barcelona 08034 (Spain)
2005-05-01
In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic-cubic or cubic-quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose-Einstein condensates supported by full or low-dimensional optical lattices. (review article)
Im, Song-Jin; Husakou, Anton; Herrmann, Joachim
2010-08-01
We study the delivery of few-cycle soliton-like pulses at 800 nm with gigawatt power or microjoule energy through a hollow-core kagome-lattice photonic crystal fiber over 1 m with preserved temporal and spectral shape. We show that with optimized pressure of the argon filling, 5 fs input pulses are compressed up to 2.5 fs after 20 cm and restore their shape after 1 m propagation.
Institute of Scientific and Technical Information of China (English)
Dong Huan-He
2007-01-01
A direct way to construct integrable couplings for discrete systems is presented by use of two semi-direct sum Lie algebras. As their applications, the discrete integrable couplings associated with modified Korteweg-de Vries (m-KdV) lattice and two hierarchies of discrete soliton equations are developed. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards the complete classification of integrable couplings.
Liu, De-Yin; Tian, Bo; Xie, Xi-Yang
2017-03-01
Bound-state vector soliton solutions for the coupled variable-coefficient higher-order nonlinear Schrödinger equations, which describe the simultaneous propagation of nonlinear waves in the inhomogeneous optical fiber, are investigated. Introducing auxiliary functions, we derive the bilinear forms and corresponding constraints on the variable coefficients. Through symbolic computation, we construct the one- and two-soliton solutions. We see that the variable coefficients in the equations affect the soliton structures. With different choices of the variable coefficients, we obtain the cubic, periodic, and parabolic solitons. Bound-state solitons and interactions are analyzed graphically.
Soliton solution for nonlinear partial differential equations by cosine-function method
Energy Technology Data Exchange (ETDEWEB)
Ali, A.H.A. [Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom (Egypt); Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt)], E-mail: asoliman_99@yahoo.com; Raslan, K.R. [Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo (Egypt)
2007-08-20
In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations.
Self-trapping transition in nonlinear cubic lattices
Naether, Uta; Guzmán-Silva, Diego; Molina, Mario I; Vicencio, Rodrigo A
2013-01-01
We explore the fundamental question about the critical nonlinearity value needed to dynamically localize energy in discrete nonlinear cubic (Kerr) lattices. We focus on the effective frequency and participation ratio of the profile to determine the transition into localization, performing several numerical simulations in one-, two-, and three-dimensional lattices. A simple criterium is developed - for the case of an initially localized excitation - defining the transition region in parameter space ("dynamical tongue") from a delocalized to a localized profile. A general analytical estimate of the critical nonlinearity value for which this transition occurs is obtained.
Indian Academy of Sciences (India)
M Lakshmanan; T Kanna
2001-11-01
Coupled nonlinear Schrödinger equations (CNLS) very often represent wave propagation in optical media such as multicore ﬁbers, photorefractive materials and so on. We consider speciﬁcally the pulse propagation in integrable CNLS equations (generalized Manakov systems). We point out that these systems possess novel exact soliton type pulses which are shape changing under collision leading to an intensity redistribution. The shape changes correspond to linear fractional transformations allowing for the possibility of construction of logic gates and Turing equivalent all optical computers in homogeneous bulk media as shown by Steiglitz recently. Special cases of such solitons correspond to the recently much discussed partially coherent stationary solitons (PCS). In this paper, we review critically the recent developments regarding the above properties with particular reference to 2-CNLS.
Institute of Scientific and Technical Information of China (English)
Cao Wen-Jun; Xu Wen-Cheng; Luo Zhi-Chao; Wang Lu-Yan; Wang Hui-Yi; Dong Jiang-Li; Luo Ai-Ping
2011-01-01
We report on the generation of dual-wavelength dissipative solitons in a passively mode-locked fibre laser with a net normal dispersion using the nonlinear polarization rotation (NPR) technique.Taking the intrinsic advantage of the intracavity birefringence-induced spectral filtering effect in the NPR-based ring laser cavity,the dual-wavelength dissipative solitons are obtained.In addition,the wavelength separation and the lasing location of the dual-wavelength solitons can be flexibly tuned by changing the orientation of the polarization controller.
Schrödinger plasmon-solitons in Kerr nonlinear heterostructures with magnetic manipulation.
Davydova, M D; Dodonov, D V; Kalish, A N; Belotelov, V; Zvezdin, A K
2015-12-01
We investigate surface plasmon-soliton (SPS) propagation in transverse magnetic field in heterostructures with Kerr nonlinearity. The nonlinear Schrödinger equation in the framework of perturbation theory has been derived for three cases: a single-interface metal/nonlinear-dielectric structure and double-interface structures of nonlinear-dielectric/metal/dielectric with either ferromagnetic or nonmagnetic dielectric. The effect of the magneto-optical nonreciprocity in the Schrödinger equation is found. The estimations show that the effect is the strongest for the double-interface structure with a magnetic substrate in the vicinity of the resonant plasmonic frequency. We have also shown that the external magnetic field modifies SPS amplitude and width.
Johansson, Magnus; Derevyanko, Stanislav A
2013-01-01
We investigate the mobility of nonlinear localized modes in a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping, described by a generalized discrete Ginzburg-Landau type model. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations, and slower, large-oscillation modes. The velocities and the oscillation periods are typically related...
Nonlinear switching and solitons in PT-symmetric photonic systems
Suchkov, Sergey V; Huang, Jiahao; Dmitriev, Sergey V; Lee, Chaohong; Kivshar, Yuri S
2015-01-01
One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity-Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensity-dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonl...
Solitons riding on solitons and the quantum Newton's cradle
Ma, Manjun; Navarro, R.; Carretero-González, R.
2016-02-01
The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves corresponding to Toda lattice solitons. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. It is observed that in the case of dark soliton chains, the formulated reduction dynamics provides an accurate an robust evolution of traveling hypersolitons. As an application to Bose-Einstein condensates trapped in a standard harmonic potential, we study the case of a finite dark soliton chain confined at the center of the trap. When the central chain is hit by a dark soliton, the energy is transferred through the chain as a hypersoliton that, in turn, ejects a dark soliton on the other end of the chain that, as it returns from its excursion up the trap, hits the central chain repeating the process. This periodic evolution is an analog of the classical Newton's cradle.
Optical Solitons in a Trinal-channel Inverted Nonlinear Photonic Crystal
Chen, Guihua; Wu, Muying
2014-01-01
Inverted nonlinear photonic crystals are the crystals featuring competition between linear and nonlinear lattices, with minima of the linear potential coinciding with maxima of the nonlinear pseudopotential, and vice versa. Traditional inverted nonlinear photonic crystals only have two channels, and can be attained experimentally by means of Rhodamine B (RhB, a dye featuring saturable absorption) doped into the SU-8 polymer. In this paper, a new type of inverted nonlinear photonic crystal is constructed by juxtaposing three kinds of channels into a period. These three channels are a purely linear channel, a saturable self-focusing nonlinear channel, and a saturable self-defocusing nonlinear channel. This optical device is assumed to be fabricated by means of SU-8 polymer material periodically doped with two types of active dyes. The nonlinear propagation of a light field inside this device (passing along the channel) can be described by a nonlinear Schrodinger equation. Stable multi-peak fundamental and dipol...
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
Feijoo, David; Konotop, Vladimir V
2016-01-01
We analyze a system of three two-dimensional nonlinear Schr\\"odinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time ($\\mathcal{PT}$) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the $\\mathcal{PT}$-symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and $\\mathcal{PT}$-symmetric cases. Interactions and collisions between the conservative and $\\mathcal{PT}$-symmetric solitons are briefly investigated, as well.
Nonlinear quantum piston for the controlled generation of vortex rings and soliton trains
Pinsker, Florian
2013-05-29
We propose a simple way to generate nonlinear excitations in a controllable way by managing interactions in Bose-Einstein condensates. Under the action of a quantum analog of a classical piston, the condensed atoms are pushed through the trap, generating vortex rings infully three-dimensional condensates or soliton trains in quasi-one-dimensional scenarios. The vortex rings form due to transverse instability of the shock-wave train, enhanced and supported by the energy transfer between waves. We elucidate in what sense the self-interactions within the atom cloud define the properties of the generated vortex rings and soliton trains. Based on the quantum-piston scheme we study the behavior of two-component Bose-Einstein condensates and analyze how the presence of an additional superfluid influences the generation of vortex rings or solitons in the other component, and vice versa. Finally, we show the dynamical emergence of skyrmions within two-component systems in the immiscible regime. © 2013 American Physical Society.
2006-01-29
Jakubowski, and R. Squier, “Collisions of two solitons in an arbitrary number of coupled nonlinear Schrodinger equations ”, Physical Review Letters 90...on Nonlinear Evolution Equations and Wave Phenomena, Athens, Georgia, April 11-14, 2005. 89. D. N. Christodoulides, “ Discrete solitons in...Solitons for signal processing applications: 1. Navigating discrete solitons in two-dimensional nonlinear waveguide array networks: Among
Quantum nonlinear lattices and coherent state vectors
DEFF Research Database (Denmark)
Ellinas, Demosthenes; Johansson, M.; Christiansen, Peter Leth
1999-01-01
for the CSV parameters. The so obtained evolution equations are intimately related to the respective evolution equations for the classical lattices, provided we account for the ordering rules (normal, symmetric) adopted for their quantization. Analysing the geometrical content of the factorization ansatz made...
Realization of non-linear coherent states by photonic lattices
Directory of Open Access Journals (Sweden)
Shahram Dehdashti
2015-06-01
Full Text Available In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2 and su(1, 1 coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Realization of non-linear coherent states by photonic lattices
Energy Technology Data Exchange (ETDEWEB)
Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn [State Key Laboratory of Modern Optical Instrumentations, Zhejiang University, Hangzhou 310027 (China); The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027 (China); Liu, Jiarui, E-mail: jrliu@zju.edu.cn; Yu, Faxin [School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027 (China)
2015-06-15
In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Quasi-integrability in the modified defocusing non-linear Schr\\"odinger model and dark solitons
Blas, H
2015-01-01
The concept of quasi-integrability has been examined in the context of deformations of the defocusing non-linear Schr\\"odinger model (NLS). Our results show that the quasi-integrability concept, recently discussed in the context of deformations of the sine-Gordon, Bullough-Dodd and focusing NLS models, holds for the modified defocusing NLS model with dark soliton solutions and it exhibits the new feature of an infinite sequence of alternating conserved and asymptotically conserved charges. For the special case of two dark soliton solutions, where the field components are eigenstates of a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved in the scattering process of the solitons. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. We perform extensive numerical simulations and consider the scattering of dark solitons for the cubic-quintic NLS model with potentia...
Liu, Xing; Guo, Hairun; Bache, Morten
2015-01-01
We show numerically that ultrashort self-defocusing temporal solitons colliding with a weak pulsed probe in the near-IR can convert the probe to the mid-IR. A near-perfect conversion efficiency is possible for a high effective soliton order. The near-IR self-defocusing soliton can form in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between $\\lambda=2.2-2.4~\\mu\\rm m$ as a resonant dispersive wave. This process relies on non-degenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation.
Nonlinear feedback control of spatiotemporal chaos in coupled map lattices
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
1998-01-01
Full Text Available We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos. The method is illustrated by the coupled map lattices with five different connection forms. A key issue addressed is to find nonlinear feedback functions. Two large types of nonlinear feedback functions are introduced. The efficient and robustness of the method based on the flexibility of choices of nonlinear feedback functions are discussed. Various numerical results of nonlinear control are given. We have not found any difficulty for study both of control and synchronization using nonlinear feedback functional method. The method can also be extended to time continuous dynamical systems as well as to society problems.
Zhang, Han
2011-01-01
Solitons, as stable localized wave packets that can propagate long distance in dispersive media without changing their shapes, are ubiquitous in nonlinear physical systems. Since the first experimental realization of optical bright solitons in the anomalous dispersion single mode fibers (SMF) by Mollenauer et al. in 1980 and optical dark solitons in the normal dispersion SMFs by P. Emplit et al. in 1987, optical solitons in SMFs had been extensively investigated. In reality a SMF always supports two orthogonal polarization modes. Taking fiber birefringence into account, it was later theoretically predicted that various types of vector solitons, including the bright-bright vector solitons, dark-dark vector solitons and dark-bright vector solitons, could be formed in SMFs. However, except the bright-bright type of vector solitons, other types of vector solitons are so far lack of clear experimental evidence. Optical solitons have been observed not only in the SMFs but also in mode locked fiber lasers. It has be...
Influence of solitons on the transition to spatiotemporal chaos in coupled map lattices
DEFF Research Database (Denmark)
Mikkelsen, R.; van Hecke, M.; Bohr, Tomas
2003-01-01
absorbing states; we present evidence obtained from the study of bulk properties and the spreading of chaotic seeds in a laminar background. To study the influence of the solitons more specifically, we introduce a soliton including variant of the stochastic Domany-Kinzel cellular automaton. Similar...... to the deterministic model, we find a transition from second- to first-order behavior due to the solitons, both in a mean-field analysis and in a numerical study of the statistical properties of this stochastic model. Our study illustrates that under the appropriate mapping some deterministic chaotic systems behave...
Indian Academy of Sciences (India)
Miki Wadati
2001-11-01
As an introduction to the special issue on nonlinear waves, solitons and their signiﬁcance in physics are reviewed. The soliton is the ﬁrst universal concept in nonlinear science. Universality and ubiquity of the soliton concept are emphasized.
Solitonic and chaotic behaviors for the nonlinear dust-acoustic waves in a magnetized dusty plasma
Zhen, Hui-Ling; Tian, Bo; Xie, Xi-Yang; Wu, Xiao-Yu; Wen, Xiao-Yong
2016-05-01
A model for the nonlinear dust-ion-acoustic waves in a two-ion-temperature, magnetized dusty plasma is studied in this paper. Via the symbolic computation, one-, two- and N-soliton solutions are obtained. It is found that when √{μeμi }parallel during the propagation on the x - y, x - t, and y - t planes, where x, y, and z are the scaled spacial coordinates, and t is the retarded time. Upon the introduction of the driving force Γ(t ) , both the developed and weak chaotic motions as well as the effect of Γ(t ) are explored. Via the phase projections and power spectra, we find the difference between the two chaotic motions roots in the relative magnitude of nonlinearity and external force. Increasing the frequency of the external force or the strength of the damped term can weaken the chaotic motions of such a forced model.
Hofstadter butterflies in nonlinear Harper lattices, and their optical realizations
Energy Technology Data Exchange (ETDEWEB)
Manela, Ofer; Segev, Mordechai [Department of Physics and Solid State Institute, Technion, Haifa 32000 (Israel); Christodoulides, Demetrios N [College of Optics/CREOL, University of Central Florida, FL 32816-2700 (United States); Kip, Detlef, E-mail: msegev@tx.technion.ac.i [Department of Electrical Engineering, Helmut Schmidt University, 22043 Hamburg (Germany)
2010-05-15
The ubiquitous Hofstadter butterfly describes a variety of systems characterized by incommensurable periodicities, ranging from Bloch electrons in magnetic fields and the quantum Hall effect to cold atoms in optical lattices and more. Here, we introduce nonlinearity into the underlying (Harper) model and study the nonlinear spectra and the corresponding extended eigenmodes of nonlinear quasiperiodic systems. We show that the spectra of the nonlinear eigenmodes form deformed versions of the Hofstadter butterfly and demonstrate that the modes can be classified into two families: nonlinear modes that are a 'continuation' of the linear modes of the system and new nonlinear modes that have no counterparts in the linear spectrum. Finally, we propose an optical realization of the linear and nonlinear Harper models in transversely modulated waveguide arrays, where these Hofstadter butterflies can be observed. This work is relevant to a variety of other branches of physics beyond optics, such as disorder-induced localization in ultracold bosonic gases, localization transition processes in disordered lattices, and more.
Nonlinear accelerator lattices with one and two analytic invariants
Energy Technology Data Exchange (ETDEWEB)
Danilov, V.; /SNS Project, Oak Ridge; Nagaitsev, S.; /Fermilab
2010-02-01
Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear nonintegrable mapping produces chaotic motion and a complex network of stable and unstable resonances. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice one has to find magnetic and electric field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents 3 families of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.
Nonlinear Realization of Chiral Symmetry on the Lattice
Chandrasekharan, S; Steffen, F D; Wiese, U J
2003-01-01
We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the doubler fermions while maintaining exact chiral symmetry on the lattice. Our lattice formulation enables us to address non-perturbative questions in effective field theories of baryons interacting with pions and in models involving constituent quarks interacting with pions and gluons. We show that a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering complex action problems. In our formulation one can also decide non-perturbatively if the chiral quark model of Georgi and Manohar provides an appropriate low-energy description of QCD. If so, one could understand why the non-relativistic quark model works.
Blas, H; Vilela, A M
2016-01-01
Deformations of the focusing non-linear Schr\\"odinger model (NLS) are considered in the context of the quasi-integrability concept. We strengthen the results of JHEP09(2012)103 for bright soliton collisions. We addressed the focusing NLS as a complement to the one in JHEP03(2016)005, in which the modified defocusing NLS models with dark solitons were shown to exhibit an infinite tower of exactly conserved charges. We show, by means of analytical and numerical methods, that for certain two-bright-soliton solutions, in which the modulus and phase of the complex modified NLS field exhibit even parities under a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved during the scattering process of the solitons. We perform extensive numerical simulations and consider the bright solitons with deformed potential $ V = \\frac{ 2\\eta}{2+ \\epsilon} \\( |\\psi|^2\\)^{2 + \\epsilon}, \\epsilon \\in \\IR, \\eta<0$. However, for two-soliton field components without definite parity ...
Solitons and Scattering for the Cubic-Quintic Nonlinear Schrödinger Equation on R^3
Killip, Rowan; Oh, Tadahiro; Pocovnicu, Oana; Vişan, Monica
2017-07-01
We consider the cubic-quintic nonlinear Schrödinger equation: ipartial_t u = -Δ u - |u|^2u + |u|^4u. In the first part of the paper, we analyze the one-parameter family of ground state solitons associated to this equation with particular attention to the shape of the associated mass/energy curve. Additionally, we are able to characterize the kernel of the linearized operator about such solitons and to demonstrate that they occur as optimizers for a one-parameter family of inequalities of Gagliardo-Nirenberg type. Building on this work, in the latter part of the paper we prove that scattering holds for solutions belonging to the region R of the mass/energy plane where the virial is positive. We show that this region is partially bounded by solitons also by rescalings of solitons (which are not soliton solutions in their own right). The discovery of rescaled solitons in this context is new and highlights an unexpected limitation of any virial-based methodology.
Excitation Thresholds for Nonlinear Localized Modes on Lattices
Weinstein, M I
1999-01-01
Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schrödinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schrödinger systems (DNLS). We prove that if $\\sigma\\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, the context of DNLS. We also discuss upper and lower bounds for excitation threshol...
Brambila, Danilo
2012-05-01
Quantum chaos has emerged in the half of the last century with the notorious problem of scattering of heavy nuclei. Since then, theoreticians have developed powerful techniques to approach disordered quantum systems. In the late 70\\'s, Casati and Chirikov initiated a new field of research by studying the quantum counterpart of classical problems that are known to exhibit chaos. Among the several quantum-classical chaotic systems studied, the kicked rotor stimulated a lot of enthusiasm in the scientific community due to its equivalence to the Anderson tight binding model. This equivalence allows one to map the random Anderson model into a set of fully deterministic equations, making the theoretical analysis of Anderson localization considerably simpler. In the one-dimensional linear regime, it is known that Anderson localization always prevents the diffusion of the momentum. On the other hand, for higher dimensions it was demonstrated that for certain conditions of the disorder parameter, Anderson localized modes can be inhibited, allowing then a phase transition from localized (insulating) to delocalized (metallic) states. In this thesis we will numerically and theoretically investigate the properties of a multidimensional quantum kicked rotor in a nonlinear medium. The presence of nonlinearity is particularly interesting as it raises the possibility of having soliton waves as eigenfunctions of the systems. We keep the generality of our approach by using an adjustable diffusive nonlinearity, which can describe several physical phenomena. By means of Variational Calculus we develop a chaotic map which fully describes the soliton dynamics. The analysis of such a map shows a rich physical scenario that evidences the wave-particle behavior of a soliton. Through the nonlinearity, we trace a correspondence between quantum and classical mechanics, which has no equivalent in linearized systems. Matter waves experiments provide an ideal environment for studying Anderson
Bright and gap solitons in membrane-type acoustic metamaterials
Zhang, Jiangyi; Romero-García, Vicente; Theocharis, Georgios; Richoux, Olivier; Achilleos, Vassos; Frantzeskakis, Dimitrios J.
2017-08-01
We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive, and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement.
Liu, Lei; Tian, Bo; Xie, Xi-Yang; Guan, Yue-Yang
2017-01-01
Studied in this paper are the vector bright solitons of the coupled higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber. With the help of auxiliary functions, we obtain the bilinear forms and construct the vector bright one- and two-soliton solutions via the Hirota method and symbolic computation. Two types of vector solitons are derived. Single-hump, double-hump, and flat-top solitons are displayed. Elastic and inelastic interactions between the Type-I solitons, between the Type-II solitons, and between the two combined types of the solitons are revealed, respectively. Especially, from the interaction between a Type-I soliton and a Type-II soliton, we see that the Type-II soliton exhibits the oscillation periodically before such an interaction and becomes the double-hump soliton after the interaction, which is different from the previously reported.
Solitons and rogue waves for a nonlinear system in the geophysical fluid
Xie, Xi-Yang; Tian, Bo; Liu, Lei; Wu, Xiao-Yu; Jiang, Yan
2016-12-01
In this paper, we investigate a nonlinear system, which describes the marginally unstable baroclinic wave packets in the geophysical fluid. Based on the symbolic computation and Hirota method, bright one- and two-soliton solutions for such a system are derived. Propagation and collisions of the solitons are graphically shown and discussed with β, which reflects the collision between the wave packet and mean flow, α, which measures the state of the basic flow, and group velocity γ. γ is observed to affect the amplitudes of the solitons, and α can influence the solitons’ traveling directions. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions are derived. Properties of the first- and second-order rogue waves are graphically presented and analyzed: The first-order rogue waves are shown in the figures. α has no effects on A, which is the amplitude of the wave packet, but with the increase of α, amplitude of B, which is a quantity measuring the correction of the basic flow, decreases. When β is chosen differently, A and B do not keep their shapes invariant. With the value of γ increasing, amplitudes of A and B become larger. The second-order rogue wave is presented, from which we observe that with α increasing, amplitude of B decreases, but α has no effects on A. Collision features of A and B alter with the value of β changing. When we make the value of γ larger, amplitudes of A and B increase.
Directory of Open Access Journals (Sweden)
Yi-Xiang Chen
Full Text Available Two families of Gaussian-type soliton solutions of the (n+1-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials are analytically derived. As an example, we discuss some dynamical behaviors of two dimensional soliton solutions. Their phase switches, powers and transverse power-flow densities are discussed. Results imply that the powers flow and exchange from the gain toward the loss regions in the PT cell. Moreover, the linear stability analysis and the direct numerical simulation are carried out, which indicates that spatial Gaussian-type soliton solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the defocusing cubic and focusing power-law nonlinear medium, while they are always unstable for all parameters in other media.
Elimination of Nonlinear Deviations in Thermal Lattice BGK Models
Chen, Y; Hongo, T; Chen, Yu; Ohashi, Hirotada; Akiyam, Mamoru
1993-01-01
Abstracet: We present a new thermal lattice BGK model in D-dimensional space for the numerical calculation of fluid dynamics. This model uses a higher order expansion of equilibrium distribution in Maxwellian type. In the mean time the lattice symmetry is upgraded to ensure the isotropy of 6th order tensor. These manipulations lead to macroscopic equations free from nonlinear deviations. We demonstrate the improvements by conducting classical Chapman-Enskog analysis and by numerical simulation of shear wave flow. The transport coefficients are measured numerically, too.
Energy Technology Data Exchange (ETDEWEB)
Vakhnenko, Oleksiy O., E-mail: vakhnenko@bitp.kiev.ua
2016-05-27
Highlights: • The integrable nonlinear Schrödinger system on a triangular-lattice ribbon is inclined to metamorphoses. • The system under study is capable to incorporate the effect of external linear potential. • The system criticality against the background parameter reduces the number of independent field variables. • At critical point the system Poisson structure becomes degenerate. • The effect of criticality is elucidated by the system one-soliton solution. - Abstract: The variativity of governing coupling parameters in the integrable nonlinear Schrödinger system on a triangular-lattice ribbon is shown to ensure the important qualitative rearrangements in the system dynamics. There are at least the two types of system crucial modifications stipulated by the two types of governing parameters. Thus the longitudinal coupling parameters regulated mainly by the background values of concomitant field variables are responsible for the bifurcation of primary integrable nonlinear system into the integrable nonlinear system of Ablowitz–Ladik type. As a consequence in a critical point the number of independent field variables is reduced by a half and the system Poisson structure turns out to be degenerate. On the other hand the transverse coupling parameters regulated basically by the choice of their a priori arbitrary dependencies on time are capable to incorporate the effect of external linear potential. As a consequence the primary integrable nonlinear system with appropriately adjusted parametrical driving becomes isomorphic to the system modeling the Bloch oscillations of charged nonlinear carriers in an electrically biased ribbon of triangular lattice. The multi-component structure of basic integrable system alongside with the attractive character of system nonlinearities has predetermined the logic of whole consideration.
Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
Kartashov, Y V; Shnir, Y; Torner, L
2014-01-01
Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist, s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical axis m, appear in many fields, including the field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multi-component systems, or as trapped quasi-linear modes in toroidal potentials. We uncover that stable solitons with this structure can be created, without any linear potential, in the single-component setting with the strength of repulsive nonlinearity growing fast enough from the center to the periphery, for both steep and smooth modulation profiles. Toroidal modes with s=1 and vorticity m=0,1,2 are produced. They are stable for m1. An approximate analytical solution is obtained for the twisted ring with s=1, m=0. Under the application of an external torque, it rotates like a solid ring. The setting can be implemented...
Gang, Zhou
2008-01-01
Nonlinear Schrodinger / Gross-Pitaevskii equations play a central role in the understanding of nonlinear optical and macroscopic quantum systems. The large time dynamics of such systems is governed by interactions of the nonlinear ground state manifold, discrete neutral modes (``excited states'') and dispersive radiation. Systems with symmetry, in spatial dimensions larger than one, typically have degenerate neutral modes. Thus, we study the large time dynamics of systems with degenerate neutral modes. This requires a new normal form (nonlinear matrix Fermi Golden Rule) governing the system's large time asymptotic relaxation to the ground state (soliton) manifold.
Institute of Scientific and Technical Information of China (English)
Yang Hong; Tang Yi
2008-01-01
We investigate the energy exchange between (3+1)D colliding spatiotemporal solitons (STSs) in dispersive media with cubic-quintic (CQ) nonlinearity by numerical simulations. Energy exchange between two (3+l)D head on colliding STSs caused by their phase difference is observed, just as occurring in other optical media. Moreover, energy exchange between two head-on colliding STSs with different speeds is firstly shown in the CQ and saturable media.This phenomenon, we believe, may arouse some interest in the future studies of soliton collision in optical media.
Experimental Evidence of Directivity-Enhancing Mechanisms in Nonlinear Lattices
Ganesh, R
2016-01-01
In this letter, we experimentally investigate the directional characteristics of propagating, finite-amplitude wave packets in lattice materials, with an emphasis on the functionality enhancement due to the nonlinearly-generated higher harmonics. To this end, we subject a thin, periodically perforated sheet to out-of-plane harmonic excitations, and we design a systematic measurement and data processing routine that leverages the full-wavefield reconstruction capabilities of a laser vibrometer to precisely delineate the effects of nonlinearity. We demonstrate experimentally that the interplay of dispersion, nonlinearity, and modal complexity which is involved in the generation and propagation of higher harmonics gives rise to secondary wave packets with characteristics that conform to the dispersion relation of the corresponding linear structure. Furthermore, these nonlinearly generated wave features display modal and directional characteristics that are complementary to those exhibited by the fundamental harm...
Nonlinear Excitation in a Ferrimagnetic Zigzag Chain
Institute of Scientific and Technical Information of China (English)
王为忠
2003-01-01
We study the nonlinear excitation(solitons)in a ferrimagnetic polymer chain by using a total Hamiltonian consisting of Su-Schrieffer-Heeger Hamiltonian and a Hubbard term.At half-filling,the distortion of lattices forms domain wall solitons,while the spin configuration forms envelope solitons.The soliton pair is obtained in a range of the electron-electron(e-e)interaction U,which depends on the electron-phonon(e-ph)interaction.The spin solitons corresponding to the left domain wall and the right domain wall of the displacement are quite different.
Solitons in one-dimensional photonic crystals
Mayteevarunyoo, Thawatchai
2008-01-01
We report results of a systematic analysis of spatial solitons in the model of 1D photonic crystals, built as a periodic lattice of waveguiding channels, of width D, separated by empty channels of width L-D. The system is characterized by its structural "duty cycle", DC = D/L. In the case of the self-defocusing (SDF) intrinsic nonlinearity in the channels, one can predict new effects caused by competition between the linear trapping potential and the effective nonlinear repulsive one. Several species of solitons are found in the first two finite bandgaps of the SDF model, as well as a family of fundamental solitons in the semi-infinite gap of the system with the self-focusing nonlinearity. At moderate values of DC (such as 0.50), both fundamental and higher-order solitons populating the second bandgap of the SDF model suffer destabilization with the increase of the total power. Passing the destabilization point, the solitons assume a flat-top shape, while the shape of unstable solitons gets inverted, with loc...
Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators
Alexeeva, N V; Tsironis, G P
2000-01-01
Chains of parametrically driven, damped pendula are known to support soliton-like clusters of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the pinning of the soliton on a "long" impurity (a longer pendulum) expands dramatically its stability region whereas "short" defects simply repel solitons producing effective partition of the chain. We also show that defects may spontaneously nucleate solitons.
Sun, Yan; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Yuan, Yu-Qiang
2017-04-01
Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with d1(z), d2(z) and d3(z), which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to d1(z), d2(z) and d3(z), respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.
An analytic map for space charge in a nonlinear lattice
Energy Technology Data Exchange (ETDEWEB)
Benedetti, C. [Dipartimento di Fisica Universita di Bologna and INFN, Via Irnerio 46, 40126 Bologna (Italy)]. E-mail: benedetti@bo.infn.it; Turchetti, G. [Dipartimento di Fisica Universita di Bologna and INFN, Via Irnerio 46, 40126 Bologna (Italy)
2005-06-13
We propose a simple analytical model for an intense beam in a lattice with localized nonlinearities. In the thin lens limit a single nonlinearity leads to a Henon like map. When the space charge is present and the core radius is small with respect to the dynamic aperture, the use of a frozen core distribution like KV is justified. In this case we define an analytic map M by composing the phase advance due to space charge, computed at the first perturbation order, with the kick due to the nonlinear force. The corresponding dynamics is almost indistinguishable from the dynamics of the 'exact' map, which requires an accurate symplectic integration, if the tune depression is weak enough. The same accuracy is preserved for parametric modulations of the perveance or the beam core radius. The extension to any other distribution is straightforward.
Classical fluid aspects of nonlinear SchrÃƒÂ¶dinger equations and solitons
Directory of Open Access Journals (Sweden)
James G. Gilson
1987-01-01
Full Text Available The author extends his alternative theory for SchrÃƒÂ¶dinger quantum mechanics by introducing the idea of energy reference strata over configuration space. It is then shown that the view from various such strata defines, the content of the system of interest and enables a variety of different descriptions of events in the same space time region. Thus according to Ã‚Â“the point of viewÃ‚Â” or energy stratum chosen so the type of SchrÃƒÂ¶dinger equation, linear or otherwise, appropriate to describe the system is determined. A nonlinear information channel between two dimensional fluid action in hyperspace into two dimensional energy hyperspace is shown to exist generally as a background to nonlinear SchrÃƒÂ¶dinger structures. In addition it is shown how soliton solutions of the one dimensional SchrÃƒÂ¶dinger equation are related to two dimensional vortex fields in hyperspace.
Interfaces Supporting Surface Gap Soliton Ground States in the 1D Nonlinear Schroedinger Equation
Dohnal, Tomas; Plum, Michael; Reichel, Wolfgang
2012-01-01
We consider the problem of verifying the existence of $H^1$ ground states of the 1D nonlinear Schr\\"odinger equation for an interface of two periodic structures: $$-u" +V(x)u -\\lambda u = \\Gamma(x) |u|^{p-1}u \\ {on} \\R$$ with $V(x) = V_1(x), \\Gamma(x)=\\Gamma_1(x)$ for $x\\geq 0$ and $V(x) = V_2(x), \\Gamma(x)=\\Gamma_2(x)$ for $x1$. The article [T. Dohnal, M. Plum and W. Reichel, "Surface Gap Soliton Ground States for the Nonlinear Schr\\"odinger Equation," \\textit{Comm. Math. Phys.} \\textbf{308}, 511-542 (2011)] provides in the 1D case an existence criterion in the form of an integral inequality involving the linear potentials $V_{1},V_2$ and the Bloch waves of the operators $-\\tfrac{d^2}{dx^2}+V_{1,2}-\\lambda$. We choose here the classes of piecewise constant and piecewise linear potentials $V_{1,2}$ and check this criterion for a set of parameter values. In the piecewise constant case the Bloch waves are calculated explicitly and in the piecewise linear case verified enclosures of the Bloch waves are computed ...
Nonlinear properties of the lattice network-based nonlinear CRLH transmission lines
Institute of Scientific and Technical Information of China (English)
王正斌; 吴昭质; 高超
2015-01-01
The nonlinear properties of lattice network-based (LNB) composite right-/left-handed transmission lines (CRLH TLs) with nonlinear capacitors are experimentally investigated. Harmonic generation, subharmonic generation, and parametric excitation are clearly observed in an unbalanced LNB CRLH TL separately. While the balanced design of the novel nonlinear TL shows that the subharmonic generation and parametric processes can be suppressed, and almost the same power level of the higher harmonics can be achieved over a wide bandwidth range, which are difficult to find in the conventional CRLH TLs.
Nonlinear light propagation in fs laser-written waveguide arrays
Directory of Open Access Journals (Sweden)
Szameit A.
2013-11-01
Full Text Available We report on recent achievements in the field of nonlinear light propagation in fs laser-written waveguide lattices. Particular emphasis is thereby given on discrete solitons in such systems.
Energy Technology Data Exchange (ETDEWEB)
Chai, Jun; Tian, Bo, E-mail: tian_bupt@163.com; Zhen, Hui-Ling; Sun, Wen-Rong
2015-08-15
Under investigation in this paper is a fifth-order nonlinear Schrödinger equation, which describes the propagation of attosecond pulses in an optical fiber. Based on the Lax pair, infinitely-many conservation laws are derived. With the aid of auxiliary functions, bilinear forms, one-, two- and three-soliton solutions in analytic forms are generated via the Hirota method and symbolic computation. Soliton velocity varies linearly with the coefficients of the high-order terms. Head-on interaction between the bidirectional two solitons and overtaking interaction between the unidirectional two solitons as well as the bound state are depicted. For the interactions among the three solitons, two head-on and one overtaking interactions, three overtaking interactions, an interaction between a bound state and a single soliton and the bound state are displayed. Graphical analysis shows that the interactions between the two solitons are elastic, and interactions among the three solitons are pairwise elastic. Stability analysis yields the modulation instability condition for the soliton solutions.
Self-trapped optical beams: Spatial solitons
Indian Academy of Sciences (India)
Andrey A Sukhorukov; Yuri S Kivshar
2001-11-01
We present a brief overview of the basic concepts of the theory ofspatial optical solitons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary waves in nonintegrable nonlinear models.
Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices
Energy Technology Data Exchange (ETDEWEB)
Rojas-Rojas, Santiago, E-mail: srojas@cefop.cl [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Naether, Uta [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, 50009 Zaragoza (Spain); Delgado, Aldo [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Vicencio, Rodrigo A. [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago (Chile)
2016-09-16
Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.
On the existence of localized excitations in nonlinear hamiltonian lattices
Flach, S
1994-01-01
We consider time-periodic nonlinear localized excitations (NLEs) on one-dimensional translationally invariant Hamiltonian lattices with arbitrary finite interaction range and arbitrary finite number of degrees of freedom per unit cell. We analyse a mapping of the Fourier coefficients of the NLE solution. NLEs correspond to homoclinic points in the phase space of this map. Using dimensionality properties of separatrix manifolds of the mapping we show the persistence of NLE solutions under perturbations of the system, provided NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam chains we rigorously prove the existence of NLE solutions.
Optical solitons in PT-symmetric nonlinear couplers with gain and loss
Alexeeva, N. V.; Barashenkov, I. V.; Sukhorukov, Andrey A.; Kivshar, Yuri S.
2012-06-01
We study spatial and temporal solitons in the PT symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain-loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space, thereby blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.
Optical solitons in $\\mathcal{PT}$-symmetric nonlinear couplers with gain and loss
Alexeeva, N V; Sukhorukov, Andrey A; Kivshar, Yuri S
2012-01-01
We study spatial and temporal solitons in the $\\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain/loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.
Nonlinear dynamics of a soliton gas: Modified Korteweg-de Vries equation framework
Shurgalina, E. G.; Pelinovsky, E. N.
2016-05-01
Dynamics of random multi-soliton fields within the framework of the modified Korteweg-de Vries equation is considered. Statistical characteristics of a soliton gas (distribution functions and moments) are calculated. It is demonstrated that the results sufficiently depend on the soliton gas properties, i.e., whether it is unipolar or bipolar. It is shown that the properties of a unipolar gas are qualitatively similar to the properties of a KdV gas [Dutykh and Pelinovsky (2014) [1
Energy Technology Data Exchange (ETDEWEB)
Alvarado-Mendez, E.; Torres-Cisneros, M.; Gutierrez-Hernandez, D. A.; Andrade-Lucio, J. A.; Rojas-Lagunas, R.; Pedraza-Ortega, J. C.; Torres Cisneros, G. E. [Universidad de Guanajuato, Guanajuato (Mexico); Sanchez Mondragon, J. J. [Universidad Autonoma del Estado de Morelos, Morelos (Mexico); Flores-Alvarado, G. [Preparatoria por Cooperacion Domingo Arenas, Tlaxcala (Mexico)
2001-06-01
We study the reflection of one-dimensional spatial soliton at the nonlinear interface between a saturable type medium and linear medium. Our study makes emphasis on determining the physical conditions under which the beam reflected by the interface is still a spatial soliton. Depended the incidence angle we find three critical regions for spatial solitons in the interface. We observed nonlinear Goos- Haechen shift is determined if reflection angle are conserved. Finally, we present preliminary experimental results in SBN61:Ce of the total internal reflection of one dimensional beam. [Spanish] Estudiamos la reflexion de un soliton espacial unidimensional en una interfase formada por un medio no lineal saturable y un medio lineal. Nuestros estudios hacen enfasis en determinar las condiciones fisicas bajo las cuales el haz reflejado por la interfase no lineal sigue siendo soliton. Encontramos tres regiones criticas para un soliton especial en la interfase, dependiendo del valor que tome el angulo de incidencia. Asi mismo observamos corrimiento Goos-Haechen no lineal que es determinante para la conservacion del angulo de reflexion. Finalmente, presentamos resultados preliminares experimentales en SBN61:Ce de la reflexion interna total de un haz unidimensional.
Guner, Ozkan; Bekir, Ahmet; Unsal, Omer; Cevikel, Adem C.
2017-01-01
In this paper, we pay attention to the analytical method named, ansatz method for finding the exact solutions of the variable-coefficient modified KdV equation and variable coefficient diffusion-reaction equation. As a result the singular 1-soliton solution is obtained. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. This method can be extended to solve other variable coefficient nonlinear partial differential equations.
Zhong, Xian-Qiong; Zhang, Xiao-Xia; Du, Xian-Tong; Liu, Yong; Cheng, Ke
2015-10-01
The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking (OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity (QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses. Supported by the Postdoctoral Fund of China under Grant No. 2011M501402, the Key Project of Chinese Ministry of Education under Grant No. 210186, the Major Project of Natural Science Supported by the Educational Department of Sichuan Province under Grant No. 13ZA0081, the Key Project of National Natural Science Foundation of China under Grant No 61435010, and the National Natural Science Foundation of China under Grant No. 61275039
Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach.
Achilleos, V; Richoux, O; Theocharis, G; Frantzeskakis, D J
2015-02-01
We report experimental results and study theoretically soliton formation and propagation in an air-filled acoustic waveguide side loaded with Helmholtz resonators. We propose a theoretical modeling of the system, which relies on a transmission-line approach, leading to a nonlinear dynamical lattice model. The latter allows for an analytical description of the various soliton solutions for the pressure, which are found by means of dynamical systems and multiscale expansion techniques. These solutions include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons that are observed in the experiment, as well as nonlinear Schrödinger envelope solitons, that are predicted theoretically. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.
Surface Gap Soliton Ground States for the Nonlinear Schr\\"{o}dinger Equation
Dohnal, Tomáš; Reichel, Wolfgang
2010-01-01
We consider the nonlinear Schr\\"{o}dinger equation $(-\\Delta +V(x))u = \\Gamma(x) |u|^{p-1}u$, $x\\in \\R^n$ with $V(x) = V_1(x) \\chi_{\\{x_1>0\\}}(x)+V_2(x) \\chi_{\\{x_10\\}}(x)+\\Gamma_2(x) \\chi_{\\{x_1<0\\}}(x)$ and with $V_1, V_2, \\Gamma_1, \\Gamma_2$ periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state $H^1$ solutions (surface gap soliton ground states) for $0<\\min \\sigma(-\\Delta +V)$. Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with $V\\equiv V_1, \\Gamma\\equiv \\Gamma_1$ and $V\\equiv V_2, \\Gamma\\equiv \\Gamma_2$) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators $-\\tfrac{d^2}{dx^2} +V_1(x)$ an...
Schuch, Dieter
2015-06-01
It is shown that a nonlinear reformulation of time-dependent and time-independent quantum mechanics in terms of Riccati equations not only provides additional information about the physical system, but also allows for formal comparison with other nonlinear theories. This is demonstrated for the nonlinear Burgers and Korteweg-de Vries equations with soliton solutions. As Riccati equations can be linearized to corresponding Schrödinger equations, this also applies to the Riccati equations that can be obtained by integrating the nonlinear soliton equations, resulting in a time-independent Schrödinger equation with Rosen-Morse potential and its supersymmetric partner. Because both soliton equations lead to the same Riccati equation, relations between the Burgers and Korteweg-de Vries equations can be established. Finally, a connection with the inverse scattering method is mentioned.
A nonlinear discrete integrable coupling system and its infinite conservation laws
Institute of Scientific and Technical Information of China (English)
Yu Fa-Jun
2012-01-01
We construct a nonlinear integrable coupling of discrete soliton hierarchy,and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy.As an explicit application of the method proposed in the paper,the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.
Multicolor Bound Soliton Molecule
Luo, Rui; Lin, Qiang
2015-01-01
We show a new class of bound soliton molecule that exists in a parametrically driven nonlinear optical cavity with appropriate dispersion characteristics. The composed solitons exhibit distinctive colors but coincide in time and share a common phase, bound together via strong inter-soliton four-wave mixing and Cherenkov radiation. The multicolor bound soliton molecule shows intriguing spectral locking characteristics and remarkable capability of spectrum management to tailor soliton frequencies, which may open up a great avenue towards versatile generation and manipulation of multi-octave spanning phase-locked Kerr frequency combs, with great potential for applications in frequency metrology, optical frequency synthesis, and spectroscopy.
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Wyller, John
2004-01-01
We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons.......We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons....
Ho, Keang-Po
2003-01-01
The characteristic function of soliton phase jitter is found analytically when the soliton is perturbed by amplifier noise. In additional to that from amplitude jitter, the nonlinear phase noise due to frequency and timing jitter is also analyzed. Because the nonlinear phase noise is not Gaussian distributed, the overall phase jitter is also non-Gaussian. For a fixed mean nonlinear phase shift, the contribution of nonlinear phase noise from frequency and timing jitter decreases with distance ...
Energy Technology Data Exchange (ETDEWEB)
Gao, Zhe; Gao, Yi-Tian; Su, Chuan-Qi; Wang, Qi-Min; Mao, Bing-Qing [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics
2016-04-01
Under investigation in this article is a generalised nonlinear Schroedinger-Maxwell-Bloch system for the picosecond optical pulse propagation in an inhomogeneous erbium-doped silica optical fibre. Lax pair, conservation laws, Darboux transformation, and generalised Darboux transformation for the system are constructed; with the one- and two-soliton solutions, the first- and second-order rogue waves given. Soliton propagation is discussed. Nonlinear tunneling effect on the solitons and rogue waves are investigated. We find that (i) the detuning of the atomic transition frequency from the optical pulse frequency affects the velocity of the pulse when the detuning is small, (ii) nonlinear tunneling effect does not affect the energy redistribution of the soliton interaction, (iii) dispersion barrier/well has an effect on the soliton velocity, whereas nonlinear well/barrier does not, (iv) nonlinear well/barrier could amplify/compress the solitons or rogue waves in a smoother manner than the dispersion barrier/well, and (v) dispersion barrier could ''attract'' the nearby rogue waves, whereas the dispersion well has a repulsive effect on them.
Nonlinear coherent dynamics of an atom in an optical lattice
Argonov, V Y
2006-01-01
We consider a simple model of lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. Internal dynamics of the atom is governed by the laser field which is treated to be classical with a large number of photons. Center-of-mass classical atomic motion is governed by the optical potential and the internal atomic degree of freedom. The resulting Hamilton-Schr\\"odinger equations of motion are a five-dimensional nonlinear dynamical system with two integrals of motion. The main focus of the paper is chaotic atomic motion that may be quantified strictly by positive values of the maximal Lyapunov exponent. It is shown that atom, depending on the value of its total energy, can either oscillate chaotically in a well of the optical potential or fly ballistically with weak chaotic oscillations of its momentum or wander in the optical lattice changing the direction of motion in a chaotic way. In the regime of chaotic wandering atomic...
A New Expanded Method for Solving Nonlinear Differential-difference Equation
Institute of Scientific and Technical Information of China (English)
ZHANG Shan-qing
2008-01-01
A new expanded approach is presented to find exact solutions of nonlinear differential-difference equations. As its application, the soliton solutions and periodic solutions of a lattice equation are obtained.
Lin, Ji; Ren, Bo; Li, Hua-mei; Li, Yi-Shen
2008-03-01
Two Darboux transformations of the (1+1) -dimensional Wu-Zhang (WZ) equation and the two-component Camassa-Holm (2CH) system with the reciprocal transformation are obtained. One-loop and two-loop soliton solutions and multisoliton(like) solutions of the 2CH system are obtained by using the Darboux transformations and selecting different seed solutions of the corresponding equations. The bidirectional soliton solutions of the (1+1) -dimensional WZ equation are also obtained. The interactions of two-soliton head-on and overtaking collisions for the WZ equation and the evolution of the two-soliton(-like) solutions for the 2CH system are studied.
Chen, Yong; Yan, Zhenya; Mihalache, Dumitru; Malomed, Boris A
2017-04-28
Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.
Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi
2017-05-01
This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.
Quasidiscrete microwave solitons in a split-ring-resonator-based left-handed coplanar waveguide.
Veldes, G P; Cuevas, J; Kevrekidis, P G; Frantzeskakis, D J
2011-04-01
We study the propagation of quasidiscrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split-ring resonators. By considering the relevant transmission line analog, we derive a nonlinear lattice model which is studied analytically by means of a quasidiscrete approximation. We derive a nonlinear Schrödinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasidiscrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments.
Positons: slowly diminishing analogs of solitons
Matveev, V B
2002-01-01
The introduction to the theory of positons is presented. The positons are the remote-acting analogues of solitons and represent slowly diminishing and oscillating solitons of the nonlinear integrated equations of KdV type. The positon and soliton-positon solutions of the KdV equation were for the first time obtained and analyzed about 10 years ago and thereafter designed for a number of other models: mKdV, Toda chains, NSch, sn-Gordon equation and its lattice analog. By the proper selection of the scattering data the single positon and multipositon potentials are characterized by the remarkable property: the corresponding reflection coefficient is equal to zero and the transition coefficient is equal to one (the latter property, as it is known, has no place for the standard short-acting nonreflection potentials
DEFF Research Database (Denmark)
Liu, Xing; Zhou, Binbin; Guo, Hairun;
2015-01-01
in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between. lambda = 2.2-2.4 mu m as a resonant dispersive wave. This process relies...... on nondegenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation. (C) 2015 Optical Society of America...
DEFF Research Database (Denmark)
D'ovidio, Francesco; Bohr, Henrik; Lindgård, Per-Anker
2005-01-01
We study the propagation of solitons along the hydrogen bonds of an alpha helix. Modeling the hydrogen and peptide bonds with Lennard-Jones potentials, we show that the solitons can appear spontaneously and have long lifetimes. Remarkably, even if no explicit solution is known for the Lennard-Jon...
Wave packet dynamics in one-dimensional linear and nonlinear generalized Fibonacci lattices.
Zhang, Zhenjun; Tong, Peiqing; Gong, Jiangbin; Li, Baowen
2011-05-01
The spreading of an initially localized wave packet in one-dimensional linear and nonlinear generalized Fibonacci (GF) lattices is studied numerically. The GF lattices can be classified into two classes depending on whether or not the lattice possesses the Pisot-Vijayaraghavan property. For linear GF lattices of the first class, both the second moment and the participation number grow with time. For linear GF lattices of the second class, in the regime of a weak on-site potential, wave packet spreading is close to ballistic diffusion, whereas in the regime of a strong on-site potential, it displays stairlike growth in both the second moment and the participation number. Nonlinear GF lattices are then investigated in parallel. For the first class of nonlinear GF lattices, the second moment of the wave packet still grows with time, but the corresponding participation number does not grow simultaneously. For the second class of nonlinear GF lattices, an analogous phenomenon is observed for the weak on-site potential only. For a strong on-site potential that leads to an enhanced nonlinear self-trapping effect, neither the second moment nor the participation number grows with time. The results can be useful in guiding experiments on the expansion of noninteracting or interacting cold atoms in quasiperiodic optical lattices.
Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions
Institute of Scientific and Technical Information of China (English)
FangJin－Qing; MKAli
1997-01-01
In this paper the nonlinear feedback functional method is presented for study of synchronization of spatiotemporal chaos in coupled map lattices with five connection forms.Some of nonlinear feedback functions are given.The noise effect on synchronization and sporadic nonlinear feedback are discussed.
ElNady, Khaled; Goda, Ibrahim; Ganghoffer, Jean-François
2016-09-01
The asymptotic homogenization technique is presently developed in the framework of geometrical nonlinearities to derive the large strains effective elastic response of network materials viewed as repetitive beam networks. This works extends the small strains homogenization method developed with special emphasis on textile structures in Goda et al. (J Mech Phys Solids 61(12):2537-2565, 2013). A systematic methodology is established, allowing the prediction of the overall mechanical properties of these structures in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the chosen equivalent continuum. Internal scale effects of the initially discrete structure are captured by the consideration of a micropolar effective continuum model. Applications to the large strain response of 3D hexagonal lattices and dry textiles exemplify the powerfulness of the proposed method. The effective mechanical responses obtained for different loadings are validated by FE simulations performed over a representative unit cell.
Energy Technology Data Exchange (ETDEWEB)
Maharaj, S. K. [South African National Space Agency (SANSA) Space Science, P.O. Box 32, Hermanus 7200 (South Africa); Bharuthram, R. [University of the Western Cape, Modderdam Road, Bellville 7530 (South Africa); Singh, S. V. [Indian Institute of Geomagnetism, New Panvel (West), Navi Mumbai 410218 (India); School of Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa); Lakhina, G. S. [Indian Institute of Geomagnetism, New Panvel (West), Navi Mumbai 410218 (India)
2012-07-15
Using the Sagdeev pseudopotential technique, the existence of large amplitude ion-acoustic solitons is investigated for a plasma composed of ions, and hot and cool electrons. Not only are all species treated as adiabatic fluids but the model for which inertial effects of the hot electrons is neglected whilst retaining inertia and pressure for the ions and cool electrons has also been considered. The focus of this investigation has been on identifying the admissible Mach number ranges for large amplitude nonlinear ion-acoustic soliton structures. The lower Mach number limit yields a minimum velocity for the existence of ion-acoustic solitons. The upper Mach number limit for positive potential solitons is found to coincide with the limiting value of the potential (positive) beyond which the ion number density ceases to be real valued, and ion-acoustic solitons can no longer exist. Small amplitude solitons having negative potentials are found to be supported when the temperature of the cool electrons is negligible.
Interaction of spatial photorefractive solitons
DEFF Research Database (Denmark)
Królikowski, W.; Denz, C.; Stepken, A.
1998-01-01
beam or the complete annihilation of some of them, depending on the relative phase of the interacting beams. In the case of mutually incoherent solitons, we show that the photorefractive nonlinearity leads to an anomalous interaction between solitons. Theoretical and experimental results reveal...... that a soliton pair may experience both attractive and repulsive forces; depending on their mutual separation. We also show that strong attraction leads to periodic collision or helical motion of solitons depending on initial conditions....
Filippov, Alexandre T
2010-01-01
If you have not already heard about solitons, you will sooner or later encounter them. The soliton, a solitary wave impulse preserving its shape and strikingly similar to a particle, is one of the most fascinating and beautiful phenomena in the physics of nonlinear waves. In this engaging book, the concept of the soliton is traced from the beginning of the last century to modern times, with recent applications in biology, oceanography, solid state physics, electronics, elementary particle physics, and cosmology. The main concepts and results of theoretical physics related to solitons can be ex
Two-Dimensional Toda-Heisenberg Lattice
Directory of Open Access Journals (Sweden)
Vadim E. Vekslerchik
2013-06-01
Full Text Available We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.
Chaves Filho, V. L.; Lima, R. P. A.; Lyra, M. L.
2015-06-01
We investigate the modulational instability of uniform wavepackets governed by the discrete nonlinear Schrodinger equation in finite linear chains and square lattices. We show that, while the critical nonlinear coupling χMI above which modulational instability occurs remains finite in square lattices, it decays as 1/L in linear chains. In square lattices, there is a direct transition between the regime of stable uniform wavefunctions and the regime of asymptotically localized solutions with stationary probability distributions. On the other hand, there is an intermediate regime in linear chains for which the wavefunction dynamics develops complex breathing patterns. We analytically compute the critical nonlinear strengths for modulational instability in both lattices, as well as the characteristic time τ governing the exponential increase of perturbations in the vicinity of the transition. We unveil that the interplay between modulational instability and self-trapping phenomena is responsible for the distinct wavefunction dynamics in linear and square lattices.
d'Ovidio, Francesco; Bohr, Henrik Georg; Lindgård, Per-Anker
2005-02-01
We study the propagation of solitons along the hydrogen bonds of an alpha helix. Modeling the hydrogen and peptide bonds with Lennard-Jones potentials, we show that the solitons can appear spontaneously and have long lifetimes. Remarkably, even if no explicit solution is known for the Lennard-Jones potential, the solitons can be characterized analytically with a good quantitative agreement using formulas for a Toda potential with parameters fitted to the Lennard-Jones potential. We also discuss and show the robustness of the family of periodic solutions called cnoidal waves, corresponding to phonons. The soliton phenomena described in the simulations of alpha helices may help to explain recent x-ray experiments on long alpha helices in Rhodopsin where a long lifetime of the vibrational modes has been observed.
Nonlinear science an interactive Mathematica notebook
Campbell, David K; Tanury, Thomas A
2012-01-01
This interactive Mathematica(TM) notebook provides a ready-made tool by which users can undertake their own mathematical experiments and explore the behavior of non-linear systems, from chaos in low-dimensional maps and coupled ordinary differential equations to solitons and coherent structures in nonlinear partial differential equations and "intrisic localized modes" and "discrete breathers" in extended lattice systems.
Villari, Leone Di Mauro; Biancalana, Fabio; Conti, Claudio
2016-01-01
We have very little experience of the quantum dynamics of the ubiquitous nonlinear waves. Observed phenomena in high energy physics are perturbations to linear waves, and classical nonlinear waves, like solitons, are barely affected by quantum effects. We know that solitons, immutable in classical physics, exhibit collapse and revivals according to quantum mechanics. However this effect is very weak and has never been observed experimentally. By predicting black hole evaporation Hawking first introduced a distinctly quantum effect in nonlinear gravitational physics.Here we show the existence of a general and universal quantum process whereby a soliton emits quantum radiation with a specific frequency content, and a temperature given by the number of quanta, the soliton Schwarzschild radius, and the amount of nonlinearity, in a precise and surprisingly simple way. This result may ultimately lead to the first experimental evidence of genuine quantum black hole evaporation. In addition, our results show that bla...
Chen, Mei-Dan; Li, Xian; Wang, Yao; Li, Biao
2017-06-01
With symbolic computation, some lump solutions are presented to a (3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, and 11435005, Ningbo Natural Science Foundation under Grant No. 2015A610159 and the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502 and K.C. Wong Magna Fund in Ningbo University
Energy Technology Data Exchange (ETDEWEB)
Yan, D; Kevrekidis, P G [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D J, E-mail: kevrekid@math.umass.edu [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece)
2011-10-14
In this work, we consider a model of a defocusing nonlinear Schroedinger equation with a variable nonlinearity exponent. This is motivated by the study of a superfluid Fermi gas in the Bose-Einstein condensation (BEC)-Bardeen-Cooper-Schrieffer crossover. In particular, we focus on the relevant mean-field model in the regime from BEC to unitarity and especially consider the modification of the nearly black soliton oscillation frequency due to the variation in the nonlinearity exponent in a harmonic trapping potential. The analytical expressions given as a function of the relevant nonlinearity exponent are corroborated by numerical computations and also extended past the BEC limit. (paper)
Institute of Scientific and Technical Information of China (English)
Peng Jin-Zhang; Yang Hong; Tang Yi
2009-01-01
By making use of the split-step Fourier method, this paper numerically simulates dynamical behaviors, including repulsion, fusion, scattering and spiraling of colliding (3+1)D spatiotemporal solitons in both the dispersive medium with cubic-quintic and the saturable medium. Careful comparison of the colliding behaviors in these two media is presented. Although the origin of the nonlinearities is different in these two media, the obtained results show that the dynamical behaviors are very similar. This presents additional evidence to support the supposition of universality of interactions between solitons.
Comte, J C; Marquié, P; Remoissenet, M
1999-12-01
We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.
Khare, Avinash; Samuelsen, Mogens R; Saxena, Avadh; 10.1088/1751-8113/43/37/375209
2010-01-01
We show that the two-dimensional, nonlinear Schr\\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.
Ankiewicz, Adrian
2016-07-01
Analysis of short-pulse propagation in positive dispersion media, e.g., in optical fibers and in shallow water, requires assorted high-order derivative terms. We present an infinite-order "dark" hierarchy of equations, starting from the basic defocusing nonlinear Schrödinger equation. We present generalized soliton solutions, plane-wave solutions, and periodic solutions of all orders. We find that "even"-order equations in the set affect phase and "stretching factors" in the solutions, while "odd"-order equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are complex. There are various applications in optics and water waves.
Attraction of nonlocal dark optical solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, Dragomir; Krolikowski, Wieslaw
2004-01-01
We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states...... of dark solitons. (C) 2004 Optical Society of America...
Localized structures in Kagome lattices
Energy Technology Data Exchange (ETDEWEB)
Saxena, Avadh B [Los Alamos National Laboratory; Bishop, Alan R [Los Alamos National Laboratory; Law, K J H [UNIV OF MASSACHUSETTS; Kevrekidis, P G [UNIV OF MASSACHUSETTS
2009-01-01
We investigate the existence and stability of gap vortices and multi-pole gap solitons in a Kagome lattice with a defocusing nonlinearity both in a discrete case and in a continuum one with periodic external modulation. In particular, predictions are made based on expansion around a simple and analytically tractable anti-continuum (zero coupling) limit. These predictions are then confirmed for a continuum model of an optically-induced Kagome lattice in a photorefractive crystal obtained by a continuous transformation of a honeycomb lattice.
Soliton crystals in Kerr resonators
Cole, Daniel C; Del'Haye, Pascal; Diddams, Scott A; Papp, Scott B
2016-01-01
Solitons are pulses that propagate without spreading due to a balance between nonlinearity and dispersion (or diffraction), and are universal features of systems exhibiting these effects. Solitons play an important role in plasma physics, fluid dynamics, atomic physics, biology, and optics. In the context of integrated photonics, bright dissipative cavity solitons in Kerr-nonlinear resonators are envisioned to play an important role in next-generation communication, computation, and measurement systems. Here we report the discovery of soliton crystals in Kerr resonators-collectively ordered ensembles of co-propagating solitons with discrete allowed temporal separations. Through analysis of optical spectra, we identify a complicated but discrete space of interacting soliton configurations, including crystals exhibiting vacancies (Schottky defects), shifted pulses (Frenkel defects), and superstructure. Time-domain characterization of the output-coupled soliton pulse train directly confirms our inference of the ...
Accessible solitons of fractional dimension
Energy Technology Data Exchange (ETDEWEB)
Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Belić, Milivoj [Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Zhang, Yiqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
2016-05-15
We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.
NONLINEAR DYNAMICAL BIFURCATION AND CHAOTIC MOTION OF SHALLOW CONICAL LATTICE SHELL
Institute of Scientific and Technical Information of China (English)
WANG Xin-zhi; HAN Ming-jun; ZHAO Yan-ying; ZHAO Yong-gang
2006-01-01
The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.
Directory of Open Access Journals (Sweden)
Renlong Zhou
2014-01-01
Full Text Available We have studied the excitation second-order nonlinearity through a triangular lattice perforated gold film instead of square lattice in many papers. Under the excitation of surface plasmas resonance effect, the second order nonlinearity exists in the noncentrosymmetric split-ring resonators arrays. Reflection of fundamental frequency wave through a triangular lattice perforated gold film is obtained. We also described the second harmonic conversion efficiencies in the second order nonlinear optical process with the spectra. Moreover, the electric field distributions of fundamental frequency above the gold film region are calculated. The light propagation through the holes results in the enhancement of the second order nonlinearity including second harmonic generation as well as the sum (difference frequency generation.
Energy approach to rivalry dynamics, soliton stability, and pattern formation in neuronal networks
Loxley, P. N.; Robinson, P. A.
2007-10-01
Hopfield’s Lyapunov function is used to view the stability and topology of equilibria in neuronal networks for visual rivalry and pattern formation. For two neural populations with reciprocal inhibition and slow adaptation, the dynamics of neural activity is found to include a pair of limit cycles: one for oscillations between states where one population has high activity and the other has low activity, as in rivalry, and one for oscillations between states where both populations have the same activity. Hopfield’s Lyapunov function is used to find the dynamical mechanism for oscillations and the basin of attraction of each limit cycle. For a spatially continuous population with lateral inhibition, stable equilibria are found for local regions of high activity (solitons) and for bound states of two or more solitons. Bound states become stable when moving two solitons together minimizes the Lyapunov function, a result of decreasing activity in regions between peaks of high activity when the firing rate is described by a sigmoid function. Lowering the barrier to soliton formation leads to a pattern-forming instability, and a nonlinear solution to the dynamical equations is found to be given by a soliton lattice, which is completely characterized by the soliton width and the spacing between neighboring solitons. Fluctuations due to noise create lattice vacancies analogous to point defects in crystals, leading to activity which is spatially inhomogeneous.
Excitations of the field-induced quantum soliton lattice in CuGeO_{3}
DEFF Research Database (Denmark)
Enderle, M.; Rønnow, H.M.; McMorrow, D.F.
2001-01-01
distinct excitation branches are observed, all of which are gapped. The two highest energy modes have minimum gaps at the commensurate wave vector and correspond to the creation or annihilation of soliton pairs. The third mode is incommensurate and is discussed in relation to theoretical predictions....
Bright Solitons in a PT-Symmetric Chain of Dimers
Directory of Open Access Journals (Sweden)
Omar B. Kirikchi
2016-01-01
Full Text Available We study the existence and stability of fundamental bright discrete solitons in a parity-time- (PT- symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.
Podivilov, Evgeniy V; Bednyakova, Anastasia E; Fedoruk, Mikhail P; Babin, Sergey A
2016-01-01
Dissipative solitons are stable localized coherent structures with linear frequency chirp generated in normal-dispersion mode-locked lasers. The soliton energy in fiber lasers is limited by the Raman effect, but implementation of intracavity feedback for the Stokes wave enables synchronous generation of a coherent Raman dissipative soliton. Here we demonstrate a new approach for generating chirped pulses at new wavelengths by mixing in a highly-nonlinear fiber of two frequency-shifted dissipative solitons, as well as cascaded generation of their clones forming a "dissipative soliton comb" in the frequency domain. We observed up to eight equidistant components in a 400-nm interval demonstrating compressibility from ~10 ps to ~300 fs. This approach, being different from traditional frequency combs, can inspire new developments in fundamental science and applications.
Zhang, Zhen; Koroleva, I.; Manevitch, L. I.; Bergman, L. A.; Vakakis, A. F.
2016-09-01
We study the dynamics and acoustics of a nonlinear lattice with fixed boundary conditions composed of a finite number of particles coupled by linear springs, undergoing in-plane oscillations. The source of the strongly nonlinearity of this lattice is geometric effects generated by the in-plane stretching of the coupling linear springs. It has been shown that in the limit of low energy the lattice gives rise to a strongly nonlinear acoustic vacuum, which is a medium with zero speed of sound as defined in classical acoustics. The acoustic vacuum possesses strongly nonlocal coupling effects and an orthogonal set of nonlinear standing waves [or nonlinear normal modes (NNMs)] with mode shapes identical to those of the corresponding linear lattice; in contrast to the linear case, however, all NNMs except the one with the highest wavelength are unstable. In addition, the lattice supports two types of waves, namely, nearly linear sound waves (termed "L waves") corresponding to predominantly axial oscillations of the particles and strongly nonlinear localized propagating pulses (termed "N L pulses") corresponding to predominantly transverse oscillating wave packets of the particles with localized envelopes. We show the existence of nonlinear nonreciprocity phenomena in the dynamics and acoustics of the lattice. Two opposite cases are examined in the limit of low energy. The first gives rise to nonreciprocal dynamics and corresponds to collective, spatially extended transverse loading of the lattice leading to the excitation of individual, predominantly transverse NNMs, whereas the second case gives rise to nonreciprocal acoutics by considering the response of the lattice to spatially localized, transverse impulse or displacement excitations. We demonstrate intense and recurring energy exchanges between a directly excited NNM and other NNMs with higher wave numbers, so that nonreciprocal energy exchanges from small-to-large wave numbers are established. Moreover, we show the
Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation
Pelinovsky, Dmitry
2010-01-01
Discrete solitons of the discrete nonlinear Schr\\"odinger (dNLS) equation become compactly supported in the anti-continuum limit of the zero coupling between lattice sites. Eigenvalues of the linearization of the dNLS equation at the discrete soliton determine its spectral and linearized stability. All unstable eigenvalues of the discrete solitons near the anti-continuum limit were characterized earlier for this model. Here we analyze the resolvent operator and prove that it is uniformly bounded in the neighborhood of the continuous spectrum if the discrete soliton is simply connected in the anti-continuum limit. This result rules out existence of internal modes (neutrally stable eigenvalues of the discrete spectrum) of such discrete solitons near the anti-continuum limit.
Excitations and management of the nonlinear localized gap modes
Indian Academy of Sciences (India)
Bishwajyoti Dey
2015-11-01
We discuss about the theory of nonlinear localized excitations, such as soliton and compactons in the gap of the linear spectrum of the nonlinear systems. We show how the gap originates in the linear spectrum using examples of a few systems, such as nonlinear lattices, Bose–Einstein condensates in optical lattice and systems represented by coupled nonlinear evolution equations. We then analytically show the excitation of solitons and compacton-like solutions in the gap of the linear spectrum of a system of coupled Korteweg–de Vries (KdV) equations with linear and nonlinear dispersions. Finally, we discuss about the theory of Feshbach resonance management and dispersion management of the soliton solutions.
Solitons: mathematical methods for physicists
Energy Technology Data Exchange (ETDEWEB)
Eilenberger, G.
1981-01-01
The book is a self-contained introduction to the theory of solitons. The Korteweg-de Vries equation is investigated and the inverse scattering transformation is treated in detail. Techniques are applied to the Toda lattice and solutions of the sine-Gordon equation. An introduction to the thermodynamics of soliton systems is given. (KAW)
Relativistic solitons and superluminal signals
Energy Technology Data Exchange (ETDEWEB)
Maccari, Attilio [Technical Institute ' G. Cardano' , Piazza della Resistenza 1, Monterotondo, Rome 00015 (Italy)]. E-mail: solitone@yahoo.it
2005-02-01
Envelope solitons in the weakly nonlinear Klein-Gordon equation in 1 + 1 dimensions are investigated by the asymptotic perturbation (AP) method. Two different types of solitons are possible according to the properties of the dispersion relation. In the first case, solitons propagate with the group velocity (less than the light speed) of the carrier wave, on the contrary in the second case solitons always move with the group velocity of the carrier wave, but now this velocity is greater than the light speed. Superluminal signals are then possible in classical relativistic nonlinear field equations.
Leech Lattice Extension of the Non-linear Schrodinger Equation Theory of Einstein spaces
Chapline, George
2015-01-01
Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of space-times with matter has remained elusive. In this note we outline how the nonlinear Schrodinger equation theory of Einstein spaces might be generalized to include matter by transplanting the theory to the 25+1 dimensional Lorentzian Leech lattice. Remarkably when a hexagonal section of the Leech lattice is set aside as the stage for the nonlinear Schrodinger equation, the discrete automorphism group of the complex Leech lattice with one complex direction fixed can be lifted to continuous Lie group symmetries. In this setting the wave function becomes an 11x11 complex matrix which represents matter degrees of freedom consisting of a 2-form abelian gauge field and vector nonabelian SU(3)xE6 gauge fields together with their supersymmetric partners. The lagrangian field equations fo...
Polymers on disordered hierarchical lattices: A nonlinear combination of random variables
Energy Technology Data Exchange (ETDEWEB)
Cook, J. (Commissariat a l' Energie Atomique, Gif-sur-Yvette (France) Univ. of Edinburgh (England)); Derrida, B. (Commissariat a l' Energie Atomique, Gif-sur-Yvette (France))
1989-10-01
The problem of directed polymers on disordered hierarchical and hypercubic lattices is considered. For the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way. The authors present the results of numerical simulations of two hierarchical lattices, finding evidence of a phase transition in one case. For a limiting case they extend the perturbation theory developed by Derrida and Griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties (overlaps) of the model. In this limit they obtain an interpolation formula, allowing one to obtain the noninteger moments of the partition function from the integer moments. They obtain bounds for the transition temperature for hierarchical and hypercubic lattices, and some similarities between the problem on the two different types of lattice are discussed.
Multi-pulse operation of a dissipative soliton fibre laser based on nonlinear polarisation rotation
Energy Technology Data Exchange (ETDEWEB)
Yu, H L; Wang, X L; Zhou, P; Chen, J B [College of Optoelectronics Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073 (China)
2016-03-31
We report an experimental observation of multiple dissipative soliton (DS) operation states in an all-normal-dispersion passively mode-locked Yb-doped fibre laser, including DS bound and oscillating states. In the bound state, multiple DSs up to 11 can coexist in the cavity. In the oscillating state, the DSs' movements are not purely random and three typical states are generalised and illustrated. A single-pulse mode-locked state is established at a high pump power by carefully adjusting the polarisation controllers. The broad spectrum indicates that it may be noise-like pulses, which can serve as a pump to generate a supercontinuum. (control of laser radiation parameters)
Nonlinear Schrodinger solitons in massive Yang-Mills theory and partial localization of Dirac matter
Maintas, X N; Diakonos, F K; Frantzeskakis, D J
2013-01-01
We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kink soliton, modulated by a plane wave, in a linear subspace transverse to the direction of free propagation. Subsequently, we explore how these solutions affect the dynamics of a Dirac field possessing an SU(2) charge. We find that this class of Yang-Mills configurations, when regarded as an external field, leads to the localization of the fermion along a line in the transverse space. Our analysis reveals a mechanism for trapping SU(2) charged fermions in the presence of an external Yang-Mills field indicating the non-abelian analogue of Landau localization in electrodynamics.
Multidimensional Localized Solitons
Boiti, M; Martina, L; Boiti, Marco
1993-01-01
Abstract: Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions. This article briefly reviews some of the main results obtained in the last five years thanks to the renewed interest in soliton theory due to this discovery. The theoretical tools needed to understand the unexpected richness of behaviour of multidimensional localized solitons during their mutual scattering are furnished. Analogies and especially discrepancies with the unidimensional case are stressed.
Formation of quasiparallel Alfven solitons
Hamilton, R. L.; Kennel, C. F.; Mjolhus, E.
1992-01-01
The formation of quasi-parallel Alfven solitons is investigated through the inverse scattering transformation (IST) for the derivative nonlinear Schroedinger (DNLS) equation. The DNLS has a rich complement of soliton solutions consisting of a two-parameter soliton family and a one-parameter bright/dark soliton family. In this paper, the physical roles and origins of these soliton families are inferred through an analytic study of the scattering data generated by the IST for a set of initial profiles. The DNLS equation has as limiting forms the nonlinear Schroedinger (NLS), Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (MKdV) equations. Each of these limits is briefly reviewed in the physical context of quasi-parallel Alfven waves. The existence of these limiting forms serves as a natural framework for discussing the formation of Alfven solitons.
Gravitating $\\sigma$ Model Solitons
Kim, Yoonbai; Moon, Sei-Hoon
1998-01-01
We study axially symmetric static solitons of O(3) nonlinear $\\sigma$ model coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are not self-dual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Ba$\\tilde n$ados-Teitelboim-Zanelli black holes with...
New Optical Solitons in High-Order Dispersive Cubic-Quintic Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
LI Hua-Mei; XU You-Shen; LIN Ji
2004-01-01
By using the generalized tanh-function method, we find bright and dark solitary wave solutions to an extended nonlinear Schrodinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonlinear terms, describing the propagation of extremely short pulses. At the same time, we also obtained other types of exact solutions.
Designing quadratic nonlinear photonic crystal fibers for soliton compression to few-cycle pulses
DEFF Research Database (Denmark)
Bache, Morten; Moses, Jeffrey; Lægsgaard, Jesper
2007-01-01
Second-harmonic generation (SHG) in the limit of large phase mismatch, given by Deltabeta=beta2-2beta1 effectively induces a Kerr-like nonlinear phase shift on the fundamental wave (FW). The phase mismatch determines the sign and magnitude of the effective Kerr nonlinearity, making large negative...
Modulation instability, solitons and beam propagation in spatially nonlocal nonlinear media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Nikolov, Nikola Ivanov
2004-01-01
We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction...
Exact bright and dark spatial soliton solutions in saturable nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain); Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: Juan.Belmonte@uclm.es; Perez-Garcia, Victor M. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)
2009-08-30
We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.
A higher order lattice BGK model for simulating some nonlinear partial differential equations
Institute of Scientific and Technical Information of China (English)
LAI HuiLin; MA ChangFeng
2009-01-01
In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux+βunux-γuxx+δuxxx= F(U). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.
A higher order lattice BGK model for simulating some nonlinear partial differential equations
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase transition point
Nixon, Sean; Yang, Jianke
2012-01-01
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena known to exist in this envelope equation are shown to also exist in the full equation including wave blowup, periodic bound states and solitary wave solutions.
A unified lattice Boltzmann model for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Chai Zhenhua [State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074 (China); Shi Baochang [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)], E-mail: sbchust@126.com; Zheng Lin [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2008-05-15
In this paper, a unified and novel lattice Boltzmann model is proposed for solving nonlinear partial differential equation that has the form DU{sub t} + {alpha}UU{sub x} + {beta}U{sup n}U{sub x} - {gamma}U{sub xx} + {delta} U{sub xxx} = F(x,t). Numerical results agree well with the analytical solutions and results derived by existing literature, which indicates the present model is satisfactory and efficient on solving nonlinear partial differential equations.
On optical solitons of the Schrödinger-Hirota equation with power law nonlinearity in optical fibers
Aslan, Ebru Cavlak; Tchier, Fairouz; Inc, Mustafa
2017-05-01
In this study, we acquire optical soliton solutions of the Schrödinger-Hirota equation (SHE) in optical fiber. The integration algorithm employed in this work is the Jacobi elliptic function (JEF). We acquire new type JEF solutions, bright and dark optical solitons that are valuable in the field of optoelectronics. Constraint conditions are presented for the obtained solitons. The results show that this method is a powerful and efficient mathematical tool for solving problems in optical fibers. The remarkable features of such solitons are demonstrated by several interesting figures.
Energy Technology Data Exchange (ETDEWEB)
Saberian, E. [Department of Physics, Faculty of Sciences, Azarbaijan Shahid Madani University, 53714-161 Tabriz (Iran, Islamic Republic of); Department of Physics, Faculty of Basic Sciences, University of Neyshabur, Neyshabur (Iran, Islamic Republic of); Esfandyari-Kalejahi, A.; Rastkar-Ebrahimzadeh, A.; Afsari-Ghazi, M. [Department of Physics, Faculty of Sciences, Azarbaijan Shahid Madani University, 53714-161 Tabriz (Iran, Islamic Republic of)
2013-03-15
The propagation of ion-acoustic (IA) solitons is studied in a plasma system, comprised of warm ions and superthermal (Kappa distributed) electrons in the presence of an electron-beam by using a hydrodynamic model. In the linear analysis, it is seen that increasing the superthermality lowers the phase speed of the IA waves. On the other hand, in a fully nonlinear investigation, the Mach number range and characteristics of IA solitons are analyzed, parametrically and numerically. It is found that the accessible region for the existence of IA solitons reduces with increasing the superthermality. However, IA solitons with both negative and positive polarities can coexist in the system. Additionally, solitary waves with both subsonic and supersonic speeds are predicted in the plasma, depending on the value of ion-temperature and the superthermality of electrons in the system. It is examined that there are upper critical values for beam parameters (i.e., density and velocity) after which, IA solitary waves could not propagate in the plasma. Furthermore, a typical interaction between IA waves and the electron-beam in the plasma is confirmed.
Energy Technology Data Exchange (ETDEWEB)
Su, Chuan-Qi; Gao, Yi-Tian; Yu, Xin [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics; Xue, Long [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics; Aviation Univ. of Air Force, Liaoning (China). Flight Training Base
2015-07-01
Under investigation in this article is a higher-order nonlinear Schroedinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.
The linear and nonlinear optical effects of white light
Institute of Scientific and Technical Information of China (English)
QI XinYuan; LIU SiMin; GUO Ru; LU Yi; GAO YuanMei; LIU ZhaoHong; HUANG ChunFu; ZHANG XiaoHua; ZHU Nan; XU JingJun
2009-01-01
An overview of our research group's experimental and theoretical developments is provided on the linear and nonlinear optical effects of white light since 2003. Their work includes the experimental researches on the white light one-dimensional photovoltaic dark spatial solitons and the waveguides and directional couplers induced by them, the circular and elliptic white-light dark spatial solitons and the white-light photorefractive phase masks, two-dimensional white-light photonic lattices and the applications of the white-light dark spatial solitons in the digital image transmission field, the interaction between the two-dimensional white-light dark spatial solitons to enhance or to improve the correlateddegree of the white light through the interaction between the white-light beam and coherent dark spatial solitons, the interaction between the one-or two-dimensional white-light dark spatial solitons and the two-dimensional white-light photonic lattices, respectively. We also numerically simulate the interaction between two or more partially incoherent bright spatial solitons and the white bright spatial soliton pairs in the saturated logarithmic nonlinear medium. We have observed experimentally for the first time,the modulation instability of the coherent light and white light, respectively, in self-defocusing medium and so on.
The linear and nonlinear optical effects of white light
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
An overview of our research group’s experimental and theoretical developments is provided on the linear and nonlinear optical effects of white light since 2003. Their work includes the experimental researches on the white light one-dimensional photovoltaic dark spatial solitons and the waveguides and directional couplers induced by them, the circular and elliptic white-light dark spatial solitons and the white-light photorefractive phase masks, two-dimensional white-light photonic lattices and the applications of the white-light dark spatial solitons in the digital image transmission field, the interaction between the two-dimensional white-light dark spatial solitons to enhance or to improve the correlated degree of the white light through the interaction between the white-light beam and coherent dark spatial solitons, the interaction between the one- or two-dimensional white-light dark spatial solitons and the two-dimensional white-light photonic lattices, respectively. We also numerically simulate the interaction between two or more partially incoherent bright spatial solitons and the white bright spatial soliton pairs in the saturated logarithmic nonlinear medium. We have observed experimentally for the first time, the modulation instability of the coherent light and white light, respectively, in self-defocusing medium and so on.
Lienard Equation and Exact Solutions for Some Soliton-Producing Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Wei-Guo; CHANG Qian-Shun; ZHANG Qi-Ren
2004-01-01
In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.
Stokes solitons in optical microcavities
Yang, Qi-Fan; Yi, Xu; Yang, Ki Youl; Vahala, Kerry
2017-01-01
Solitons are wave packets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fibre waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers, and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities, thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The discovery of a new optical soliton can impact work in other areas of photonics, including nonlinear optics and spectroscopy.
Three-wave interaction in two-component quadratic nonlinear lattices
DEFF Research Database (Denmark)
Konotop, V. V.; Cunha, M. D.; Christiansen, Peter Leth
1999-01-01
We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that. energy conversion and pulse propagation kno...
Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles
Roman Noskov; Pavel Belov; Yuri Kivshar
2012-01-01
The study of metal nanoparticles plays a central role in the emerging novel technologies employing optics beyond the diffraction limit. Combining strong surface plasmon resonances, high intrinsic nonlinearities and deeply subwavelength scales, arrays of metal nanoparticles offer a unique playground to develop novel concepts for light manipulation at the nanoscale. Here we suggest a novel principle to control localized optical energy in chains of nonlinear subwavelength metal nanoparticles bas...
Quadratic solitons as nonlocal solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole
2003-01-01
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...
Soliton resonance in bose-einstein condensate
Zak, Michail; Kulikov, I.
2002-01-01
A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.
Koller, Andrew; Olshanii, Maxim
2011-12-01
We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schrödinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form V(t) = (nh/τ)/cosh(t/τ), with n being an integer and τ being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning.
Bingzhen, Xu; Wenzheng, Wang
1995-02-01
We give a traveling-wave method for obtaining exact solutions of the modified nonlinear Schrödinger equation iut+ɛuxx+2p||u||2u +2iq(||u||2u)x=0, describing the propagation of light pulses in optical fibers, where u represents a normalized complex amplitude of a pulse envelope, t is the normalized distance along a fiber, and x is the normalized time within the frame of reference moving along the fiber at the group velocity. With the help of the ``potential function'' we obtained by this method, we find a family of solutions that are finite everywhere, particularly including periodic solutions expressed in terms of Jacobi elliptic functions, stationary periodic solutions, and ``algebraic'' soliton solutions. Compared with previous work [D. Mihalache and N. C. Panoiu, J. Math. Phys. 33, 2323 (1992)] in which two kinds of the simplest solution were given, the physical meaning of the integration constants in the potential function we give is clearer and more easily fixed with the initial parameters of the light pulse.
Solitons and periodic solutions to a couple of fractional nonlinear evolution equations
Indian Academy of Sciences (India)
M Mirzazadeh; M Eslami; Anjan Biswas
2014-03-01
This paper studies a couple of fractional nonlinear evolution equations using first integral method. These evolution equations are foam drainage equation and Klein–Gordon equation (KGE), the latter of which is considered in (2 + 1) dimensions. For the fractional evolution, the Jumarie’s modified Riemann–Liouville derivative is considered. Exact solutions to these equations are obtained.
Temporal dark polariton solitons
Kartashov, Yaroslav V
2016-01-01
We predict that strong coupling between waveguide photons and excitons of quantum well embedded into waveguide results in the formation of hybrid dark and anti-dark light-matter solitons. Such temporal solitons exist due to interplay between repulsive excitonic nonlinearity and giant group velocity dispersion arising in the vicinity of excitonic resonance. Such fully conservative states do not require external pumping to counteract losses and form continuous families parameterized by the power-dependent phase shift and velocity of their motion. Dark solitons are stable in the considerable part of their existence domain, while anti-dark solitons are always unstable. Both families exist outside forbidden frequency gap of the linear system.
Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud
2016-09-01
The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.
Institute of Scientific and Technical Information of China (English)
ZONG Feng-De; ZHANG Jie-Fang
2008-01-01
A model of the perturbed complex Toda chain (PCTC) to describe the dynamics of a Bose-Einstein condensate (BEC) N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.
Energy Technology Data Exchange (ETDEWEB)
Elton, A.B.H.
1990-09-24
A numerical theory for the massively parallel lattice gas and lattice Boltzmann methods for computing solutions to nonlinear advective-diffusive systems is introduced. The convergence theory is based on consistency and stability arguments that are supported by the discrete Chapman-Enskog expansion (for consistency) and conditions of monotonicity (in establishing stability). The theory is applied to four lattice methods: Two of the methods are for some two-dimensional nonlinear diffusion equations. One of the methods is for the one-dimensional lattice method for the one-dimensional viscous Burgers equation. And one of the methods is for a two-dimensional nonlinear advection-diffusion equation. Convergence is formally proven in the L{sub 1}-norm for the first three methods, revealing that they are second-order, conservative, conditionally monotone finite difference methods. Computational results which support the theory for lattice methods are presented. In addition, a domain decomposition strategy using mesh refinement techniques is presented for lattice gas and lattice Boltzmann methods. The strategy allows concentration of computational resources on regions of high activity. Computational evidence is reported for the strategy applied to the lattice gas method for the one-dimensional viscous Burgers equation. 72 refs., 19 figs., 28 tabs.
Measurement of nonlinear coefficient of optical fiber based on small chirped soliton transmission
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
We measure the waveform and phase curves of short optical pulses before and after transmission over different lengths of fibers by use of the pulse analyzer with the frequency-resolved optical gating (FROG),and numerically simulate pulse evolution under the experimental conditions.The nonlinear coefficient of the fiber is given by comparing the experimental results with the numerical ones.Difference between the experiment and numerical simulation is analyzed.
Dynamics of rogue waves on a multi-soliton background in a vector nonlinear Schrodinger equation
Mu, Gui; Qin, Zhenyun; Grimshaw, Roger
2014-01-01
General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free parameters are expressed in separation of variables form. These solutions exhibit rogue waves on a multisoliton background. They demonstrate that the structure of rogue waves in this two-component system is richer than that in a one-component system. The stu...
DEFF Research Database (Denmark)
Zhou, Binbin; Liu, Xing; Guo, Hairun;
2016-01-01
We experimentally observe widely tunable mid-IR femtosecond pulses by resonant radiation, generated by direct three-wave-mixing from a soliton in PPLN. The poling pitch gives a parametrically tunable resonant radiation, a feature absent in Kerr media....
Indian Academy of Sciences (India)
D Subbarao; R Uma; H Singh; Kamal Goyal; Sanjeev Goyal; Ravinder Kumar
2000-11-01
It is useful to state propagation laws for a self-focusing laser beam or a soliton in grouptheoretical form to be called Lie-optical form for being able to predict self-focusing dynamics conveniently and amongst other things, the geometrical phase. It is shown that the propagation of the gaussian laser beam is governed by a rotation group in a non-absorbing medium and by the Lorentz group in an absorbing medium if the additional symmetry of paraxial propagation is imposed on the laser beam. This latter symmetry, however, needs care in its implementation because the electromagnetic wave of the laser sees a different refractive index proﬁle than the laboratory observer in this approximation. It is explained how to estimate this non-Taylor paraxial power series approximation. The group theoretical laws so-stated are used to predict the geometrical or Berry phase of the laser beam by a technique developed by one of us elsewhere. The group-theoretical Lie-optic (or ABCD) laws are also useful in predicting the laser behavior in a more complex optical arrangement like in a laser cavity etc. The nonlinear dynamical consequences of these laws for long distance (or time) predictions are also dealt with. Ergodic dynamics of an ensemble of laser beams on the torus during absorptionless self-focusing is discussed in this context. From the point of view of new physics concepts, we introduce a stroboscopic invariant torus and a stroboscopic generating function in classical mechanics that is useful for long-distance predictions of absorptionless self-focusing.
Navarrete, Alvaro; Paredes, Angel; Salgueiro, José R.; Michinel, Humberto
2017-01-01
We analyze theoretically the Schrödinger-Poisson equation in two transverse dimensions in the presence of a Kerr term. The model describes the nonlinear propagation of optical beams in thermo-optical media and can be regarded as an analog system for a self-gravitating self-interacting wave. We compute numerically the family of radially symmetric ground-state bright stationary solutions for focusing and defocusing local nonlinearity, keeping in both cases a focusing nonlocal nonlinearity. We also analyze excited states and oscillations induced by fixing the temperature at the borders of the material. We provide simulations of soliton interactions, drawing analogies with the dynamics of galactic cores in the scalar field dark-matter scenario.
Gandzha, I S; Dutykh, D S
2015-01-01
We consider the high-order nonlinear Schr\\"odinger equation derived earlier by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope of slowly modulated gravity waves on the surface of finite-depth irrotational, inviscid, and incompressible fluid with flat bottom. This equation takes into account the third-order dispersion and cubic nonlinear dispersive terms. We rewrite this equation in dimensionless form featuring only one dimensionless parameter $kh$, where $k$ is the carrier wavenumber and $h$ is the undisturbed fluid depth. We show that one-soliton solutions of the classical nonlinear Schr\\"{o}dinger equation are transformed into quasi-soliton solutions with slowly varying amplitude when the high-order terms are taken into consideration. These quasi-soliton solutions represent the secondary modulations of gravity waves.
Thermal entanglement in 1D optical lattice chains with nonlinear coupling
Institute of Scientific and Technical Information of China (English)
Zhou Ling; Yi Xue-Xi; Song He-Shan; Guo Yan-Qing
2005-01-01
he thermal entanglement of spin-1 atoms with nonlinear coupling in an optical lattice chain is investigated for two-particle and multi-particle systems. It is found that the relation between linear coupling and nonlinear coupling is the key to determine thermal entanglement, which shows in what kinds of atoms thermal entanglement exists. This result is true both for two-particle and multi-particle systems. For multi-particle systems, the thermal entanglement does not decrease greatly, and the critical temperature decreases only slightly.
Indian Academy of Sciences (India)
ABDUL-MAJID WAZWAZ
2016-11-01
We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models.We establish the distinctdispersion relation for each equation. We use the simplified Hirota’s method to obtain multiple soliton solutions for each developed breaking soliton equation. We also develop generalized dispersion relations for the typical breaking soliton equations and the generalized negative-order breaking soliton equations. The results provide useful information on the dynamics of the relevant nonlinear negative-order equations.
Dispersion and absorption in one-dimensional nonlinear lattices: A resonance phonon approach
Xu, Lubo; Wang, Lei
2016-09-01
Based on the linear response theory, we propose a resonance phonon (r-ph) approach to study the renormalized phonons in a few one-dimensional nonlinear lattices. Compared with the existing anharmonic phonon (a-ph) approach, the dispersion relations derived from this approach agree with the expectations of the effective phonon (e-ph) theory much better. The application is also largely extended, i.e., it is applicable in many extreme situations, e.g., high frequency, high temperature, etc., where the existing one can hardly work. Furthermore, two separated phonon branches (one acoustic and one optical) with a clear gap in between can be observed by the r-ph approach in a diatomic anharmonic lattice. While only one combined branch can be detected in the same lattice with both the a-ph approach and the e-ph theory.
Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory
Harada, Koji; Kubo, Hirofumi; Yamamoto, Yuki
2009-01-01
Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.
2011-03-01
Schrödinger’s equation in dual power law media,” Physics Letters A, Vol. 372, 5941–5943, 2008. 29. Biswas, A., “Optical solitons in a parabolic law media...Agranovich, V. M., V. S. Babichenko, and V. Ya Chernyak, “Nonlinear surface polaritons,” Soviet Physics . JETP Letters , Vol. 32, 512–515, 1980. 33. Stegeman...Fibers to Photonic Crystals, Academic Press, 2003. 2. Stegeman, G. I., L. Jankovic, H. Kim, S. Polyakov , S. Carrasco, L. Torner, C. Bosshard, P. Gunter
Electrical solitons theory, design, and applications
Ricketts, David S
2010-01-01
The dominant medium for soliton propagation in electronics, nonlinear transmission line (NLTL) has found wide application as a testbed for nonlinear dynamics and KdV phenomena as well as for practical applications in ultra-sharp pulse/edge generation and novel nonlinear communication schemes in electronics. While many texts exist covering solitons in general, there is as yet no source that provides a comprehensive treatment of the soliton in the electrical domain.Drawing on the award winning research of Carnegie Mellon's David S. Ricketts, Electrical Solitons Theory, Design, and Applications i
Nonlinear Sensing With Collective States of Ultracold Atoms in Optical Lattices
2015-04-02
decimation algorithm , a method that takes into account quantum correlations. B.1. In collaboration with D. Blume and X.Y. Yin at Washington State...Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 Nonlinear quantum sensing, quantum metrology, ultracold atoms, optical lattices REPORT...with applications to interaction-based quantum metrology, Physical Review A, (10 2014): 0. doi: 10.1103/PhysRevA.90.041602 Khan W Mahmud, Lei Jiang
Frequency map analysis of resonances in a nonlinear lattice with space charge
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. E-mail: turchetti@bo.infn.it; Bazzani, A.; Bergamini, F.; Rambaldi, S.; Hofmann, I.; Bongini, L.; Franchetti, G
2001-05-21
In storage rings for heavy ion fusion beam losses must be minimized. During bunch compression high space charge is reached and the reciprocal effects between the collective modes of the beam and the single particle lattice nonlinearities must be considered to understand the problem of resonance crossing and halo formation. We show that the frequency map analysis of particle in core models gives an adequate description of the resonance network and of the chaotic regions where the halo particles can diffuse.
A New Variable-Coefficient Riccati Subequation Method for Solving Nonlinear Lattice Equations
Directory of Open Access Journals (Sweden)
Fanwei Meng
2013-01-01
Full Text Available We propose a new variable-coefficient Riccati subequation method to establish new exact solutions for nonlinear differential-difference equations. For illustrating the validity of this method, we apply it to the discrete (2 + 1-dimensional Toda lattice equation. As a result, some new and generalized traveling wave solutions including hyperbolic function solutions, trigonometric function solutions, and rational function solutions are obtained.
Dymnikova, Irina
2015-01-01
In nonlinear electrodynamics coupled to gravity, regular spherically symmetric electrically charged solutions satisfy the weak energy condition and have obligatory de Sitter centre. By the G\\"urses-G\\"ursey algorithm they are transformed to spinning electrically charged solutions asymptotically Kerr-Newman for a distant observer. Rotation transforms de Sitter center into de Sitter vacuum surface which contains equatorial disk $r=0$ as a bridge. We present general analysis of the horizons, ergoregions and de Sitter surfaces, as well as the conditions of the existence of regular solutions to the field equations. We find asymptotic solutions and show that de Sitter vacuum surfaces have properties of a perfect conductor and ideal diamagnetic, violation of the weak energy condition is prevented by the basic requirement of electrodynamics of continued media, and the Kerr ring singularity is replaced with the superconducting current.
Asymptotic reductions and solitons of nonlocal nonlinear Schr\\"{o}dinger equations
Horikis, Theodoros P
2016-01-01
Asymptotic reductions of a defocusing nonlocal nonlinear Schr\\"{o}dinger model in $(3+1)$-dimensions, in both Cartesian and cylindrical geometry, are presented. First, at an intermediate stage, a Boussinesq equation is derived, and then its far-field, in the form of a variety of Kadomtsev-Petviashvilli (KP) equations for right- and left-going waves, is found. KP models include versions of the KP-I and KP-II equations, in Cartesian and cylindrical geometry. Solitary waves solutions, planar or ring-shaped, and of dark or anti-dark type, are also predicted to occur. Their nature and stability is determined by a parameter defined by the physical parameters of the original nonlocal system. It is thus found that (dark) anti-dark solitary waves are only supported by a weak (strong) nonlocality, and are unstable (stable) in higher-dimensions. Our analytical predictions are corroborated by direct numerical simulations.
Optical Vortex Solitons in Parametric Wave Mixing
Alexander, T J; Buryak, A V; Sammut, R A; Alexander, Tristram J.; Kivshar, Yuri S.; Buryak, Alexander V.; Sammut, Rowland A.
2000-01-01
We analyze two-component spatial optical vortex solitons supported by degenerate three- or four-wave mixing in a nonlinear bulk medium. We study two distinct cases of such solitons, namely, parametric vortex solitons due to phase-matched second-harmonic generation in a optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a `halo-vortex', consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a `ring-vortex' soliton which is a vortex in a harmonic field that guides a bright localized ring-like mode of a fundamental frequency field.
Spontaneous symmetry breaking in Schr\\"{o}dinger lattices with two nonlinear sites
Brazhnyi, Valeriy A
2011-01-01
We introduce discrete systems in the form of straight (infinite) and ring-shaped chains, with two symmetrically placed nonlinear sites. The systems can be implemented in nonlinear optics (as waveguiding arrays) and BEC (by means of an optical lattice). A full set of exact analytical solutions for symmetric, asymmetric, and antisymmetric localized modes is found, and their stability is investigated in a numerical form. The symmetry-breaking bifurcation (SBB), through which the asymmetric modes emerge from the symmetric ones, is found to be of the subcritical type. It is transformed into a supercritical bifurcation if the nonlinearity is localized in relatively broad domains around two central sites, and also in the ring of a small size, i.e., in effectively nonlocal settings. The family of antisymmetric modes does not undergo bifurcations, and features both stable and unstable portions. The evolution of unstable localized modes is investigated by means of direct simulations. In particular, unstable asymmetric ...
Anderson localization and saturable nonlinearity in one-dimensional disordered lattices
Nguyen, Ba Phi
2016-01-01
We investigate numerically the propagation and the Anderson localization of plane waves in a one-dimensional lattice chain, where disorder and saturable nonlinearity are simultaneously present. Using a calculation scheme for solving the stationary discrete nonlinear Schr\\"{o}dinger equation in the fixed input case, the disorder-averaged logarithmic transmittance and the localization length are calculated in a numerically precise manner. The localization length is found to be a nonmonotonic function of the incident wave intensity, acquiring a minimum value at a certain finite intensity, due to saturation effects. For low incident intensities where the saturation effect is ineffective, the enhancement of localization due to Kerr-type nonlinearity occurs in a way similar to the case without saturation. For sufficiently high incident intensities, we find that the localization length is an increasing function of the incident wave intensity, which implies that localization is suppressed for stronger input intensiti...
Novel energy sharing collisions of multicomponent solitons
Indian Academy of Sciences (India)
T Kanna; K Sakkaravarthi; M Vijayajayanthi
2015-11-01
In this paper, we discuss the fascinating energy sharing collisions of multicomponent solitons in certain incoherently coupled and coherently coupled nonlinear Schrödinger-type equations arising in the context of nonlinear optics.
Discrete solitons in graphene metamaterials
Bludov, Yuliy V.; Smirnova, Daria A.; Kivshar, Yuri S.; Peres, N. M. R.; Vasilevskiy, Mikhail
2014-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schr\\"{o}dinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states. Fundação para a Ciência e a Tecnolog...
Discrete solitons in graphene metamaterials
Bludov, Yu. V.; Smirnova, D. A.; Kivshar, Yu. S.; Peres, N. M. R.; Vasilevskiy, M. I.
2015-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schrödinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states.
Interaction of Airy-Gaussian beams in defected photonic lattices
Shi, Zhiwei; Zhu, Xing; Xiang, Ying; Li, Huagang
2016-01-01
We investigate interactions by means of direct numerical simulations between two finite Airy-Gaussian (AiG) beams in different media with the defected photonic lattices in one transverse dimension. We discuss different lattice structures in which the beams with different intensities and phases are launched into the medium, but accelerate in opposite directions. During interactions we see the interference fringe, breathers and soliton pairs generated that are not accelerating. In the linear media, the initial deflection direction of the accelerated beams is changed by adjusting the phase shift and the beam interval. For a certain lattice period, the periodic interference fringe can form. A constructive or destructive interference can vary with the defect depth and phase shift. While the nonlinearity is introduced, the breathers is generated. Especially, the appropriate beam amplitude and lattice depth may lead to the formation of soliton pairs.
Wen, Xiao-Yong; Yan, Zhenya
2017-02-01
The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.
DEFF Research Database (Denmark)
Zhou, Binbin; Guo, Hairun; Bache, Morten
2015-01-01
and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...
DEFF Research Database (Denmark)
Zhou, Binbin; Guo, Hairun; Bache, Morten
2015-01-01
and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...... by using large-aperture crystals. The technique can readily be implemented with other crystals and laser wavelengths, and can therefore potentially replace current ultrafast frequency-conversion processes to the mid-IR....
Gravitating $\\sigma$ Model Solitons
Kim, Y; Kim, Yoonbai; Moon, Sei-Hoon
1998-01-01
We study axially symmetric static solitons of O(3) nonlinear $\\sigma$ model coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are not self-dual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Ba$\\tilde n$ados-Teitelboim-Zanelli black holes without non-Abelian scalar hair.
Breather soliton dynamics in microresonators
Yu, Mengjie; Okawachi, Yoshitomo; Griffith, Austin G; Luke, Kevin; Miller, Steven A; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L
2016-01-01
The generation of temporal cavity solitons in microresonators results in low-noise optical frequency combs which are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems with a localized temporal structure that exhibits oscillatory behavior. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here, we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation in good agreement with the numerical simulations. Our study presents experimental confirmation of the stability diagram of dissipative cavity solitons predicted by the Lugiato-Lefever equation and is importance to understandin...
Bai, Xiao-Dong; Malomed, Boris A.; Deng, Fu-Guo
2016-09-01
We consider the transfer of lattice wave packets through a tilted discrete breather (TDB) in opposite directions in the discrete nonlinear Schrödinger model with asymmetric defects, which may be realized as a Bose-Einstein condensate trapped in a deep optical lattice, or as optical beams in a waveguide array. A unidirectional transport mode is found, in which the incident wave packets, whose energy belongs to a certain interval between full reflection and full passage regions, pass the TDB only in one direction, while in the absence of the TDB, the same lattice admits bidirectional propagation. The operation of this mode is accurately explained by an analytical consideration of the respective energy barriers. The results suggest that the TDB may emulate the unidirectional propagation of atomic and optical beams in various settings. In the case of the passage of the incident wave packet, the scattering TDB typically shifts by one lattice unit in the direction from which the wave packet arrives, which is an example of the tractor-beam effect, provided by the same system, in addition to the rectification of incident waves.
Observation of attraction between dark solitons
DEFF Research Database (Denmark)
Dreischuh, A.; Neshev, D.N.; Petersen, D.E.
2006-01-01
We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems, such as ......We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems...
Lattice topology and spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays
Leykam, Daniel; Sukhorukov, Andrey A; Desyatnikov, Anton S
2015-01-01
We analyze spontaneous parametric down-conversion in various experimentally feasible 1D quadratic nonlinear waveguide arrays, with emphasis on the relationship between the lattice's topological invariants and the biphoton correlations. Nontrivial topology results in a nontrivial "winding" of the array's Bloch waves, which introduces additional selection rules for the generation of biphotons. These selection rules are in addition to, and independent of existing control using the pump beam's spatial profile and phase matching conditions. In finite lattices, nontrivial topology produces single photon edge modes, resulting in "hybrid" biphoton edge modes, with one photon localized at the edge and the other propagating into the bulk. When the single photon band gap is sufficiently large, these hybrid biphoton modes reside in a band gap of the bulk biphoton Bloch wave spectrum. Numerical simulations support our analytical results.
Lattice topology and spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays
Leykam, Daniel; Solntsev, Alexander S.; Sukhorukov, Andrey A.; Desyatnikov, Anton S.
2015-09-01
We analyze spontaneous parametric down-conversion in various experimentally feasible one-dimensional quadratic nonlinear waveguide arrays, with emphasis on the relationship between the lattice's topological invariants and the biphoton correlations. Nontrivial topology results in a nontrivial "winding" of the array's Bloch waves, which introduces additional selection rules for the generation of biphotons, independent of existing control using the pump beam's spatial profile and phase-matching conditions. In finite lattices, nontrivial topology produces single-photon edge modes, resulting in "hybrid" biphoton edge modes, with one photon localized at the edge and the other propagating into the bulk. When the single-photon band gap is sufficiently large, these hybrid biphoton modes reside in a band gap of the bulk biphoton Bloch wave spectrum. Numerical simulations support our analytical results.
Energy Technology Data Exchange (ETDEWEB)
El-Tantawy, S. A., E-mail: samireltantawy@yahoo.com [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt); Moslem, W. M., E-mail: wmmoslem@hotmail.com [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt); Centre for Theoretical Physics, The British University in Egypt (BUE), El-Shorouk City, Cairo (Egypt)
2014-05-15
Solitons (small-amplitude long-lived waves) collision and rogue waves (large-amplitude short-lived waves) in non-Maxwellian electron-positron-ion plasma have been investigated. For the solitons collision, the extended Poincaré-Lighthill-Kuo perturbation method is used to derive the coupled Korteweg-de Vries (KdV) equations with the quadratic nonlinearities and their corresponding phase shifts. The calculations reveal that both positive and negative polarity solitons can propagate in the present model. At critical value of plasma parameters, the coefficients of the quadratic nonlinearities disappear. Therefore, the coupled modified KdV (mKdV) equations with cubic nonlinearities and their corresponding phase shifts have been derived. The effects of the electron-to-positron temperature ratio, the ion-to-electron temperature ratio, the positron-to-ion concentration, and the nonextensive parameter on the colliding solitons profiles and their corresponding phase shifts are examined. Moreover, generation of ion-acoustic rogue waves from small-amplitude initial perturbations in plasmas is studied in the framework of the mKdV equation. The properties of the ion-acoustic rogue waves are examined within a nonlinear Schrödinger equation (NLSE) that has been derived from the mKdV equation. The dependence of the rogue wave profile on the relevant physical parameters has been investigated. Furthermore, it is found that the NLSE that has been derived from the KdV equation cannot support the propagation of rogue waves.
Generation of bright soliton through the interaction of black solitons
Losano, L; Bazeia, D
2001-01-01
We report on the possibility of having two black solitons interacting inside a silica fiber that presents normal group-velocity dispersion, to generate a pair of solitons, a vector soliton of the black-bright type. The model obeys a pair of coupled nonlinear Schr\\"odinger equations, that follows in accordance with a Ginzburg-Landau equation describing the anisotropic XY model. We solve the coupled equations using a trial-orbit method, which plays a significant role when the Schr\\"odinger equations are reduced to first order differential equations.
Effect of Soliton Propagation in Fiber Amplifiers
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The propagation of optical solitons in fiber amplifiers is discussed by considering a model that includes linear high order dispersion, two-photon absorption, nonlinear high-order dispersion, self-induced Ramam and five-order nonlinear effects. Based on travelling wave method, the solutions of the nonlinear Schrdinger equations, and the influence on soliton propagation as well as high-order effect in the fiber amplifier are discussed in detail. It is found that because of existing five-order nonlinear effect, the solution is not of secant hyperbola type, but shows high gain state of the fiber amplifier which is very favourable to the propagation of solitons.
Exciton-polaritons in lattices: A non-linear photonic simulator
Amo, Alberto; Bloch, Jacqueline
2016-10-01
Microcavity polaritons are mixed light-matter quasiparticles with extraordinary nonlinear properties, which can be easily accessed in photoluminescence experiments. Thanks to the possibility of designing the potential landscape of polaritons, this system provides a versatile photonic platform to emulate 1D and 2D Hamiltonians. Polaritons allow transposing to the photonic world some of the properties of electrons in solid-state systems, and to engineer Hamiltonians for photons with novel transport properties. Here we review some experimental implementations of polariton Hamiltonians using lattice geometries. xml:lang="fr"
A new model for nonlinear acoustic waves in a non-uniform lattice of Helmholtz resonators
Mercier, Jean-François
2016-01-01
Propagation of high amplitude acoustic pulses is studied in a 1D waveguide, connected to a lattice of Helmholtz resonators. An homogenized model has been proposed by Sugimoto (J. Fluid. Mech., 244 (1992)), taking into account both the nonlinear wave propagation and various mechanisms of dissipation. This model is extended to take into account two important features: resonators of different strengths and back-scattering effects. The new model is derived and is proved to satisfy an energy balance principle. A numerical method is developed and a better agreement between numerical and experimental results is obtained.
Chen, Zhiming
2016-01-01
We propose a scheme to exhibit a Stern-Gerlach effect of n-component (n > 2) high-dimensional ultraslow optical solitons in a coherent atomic system with (n + 1)-pod level configuration via electromagnetically induced transparency (EIT). Based on Maxwell-Bloch equations, we derive coupled (3+1)-dimensional nonlinear Schrodinger equations governing the spatial-temporal evolution of n probe-field envelopes. We show that under EIT condition significant deflections of the n components of coupled ultraslow optical solitons can be achieved by using a Stern-Gerlach gradient magnetic field. The stability of the ultraslow optical solitons can be realized by an optical lattice potential contributed from a far-detuned laser field.
Bright solitons in a PT-symmetric chain of dimers
Kirikchi, Omar B; Susanto, Hadi
2016-01-01
We study the existence and stability of fundamental bright discrete solitons in a parity-time (PT)-symmetric coupler composed by a chain of dimers, that is modelled by linearly coupled discrete nonlinear Schrodinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anti-continuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, on the contrary of the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quart...
Biological effects of pulsating magnetic fields: role of solitons
Brizhik, Larissa
2014-01-01
In this paper, we analyze biological effects produced by magnetic fields in order to elucidate the physical mechanisms, which can produce them. We show that there is a chierarchy of such mechanisms and that the mutual interplay between them can result in the synergetic outcome. In particular, we analyze the biological effects of magnetic fields on soliton mediated charge transport in the redox processes in living organisms. Such solitons are described by nonlinear systems of equations and represent electrons that are self-trapped in alpha-helical polypeptides due to the moderately strong electron-lattice interaction. They represent a particular type of disssipativeless large polarons in low-dimensional systems. We show that the effective mass of solitons in the is different from the mass of free electrons, and that there is a resonant effect of the magnetic fields on the dynamics of solitons, and, hence, on charge transport that accompanies photosynthesis and respiration. These effects can result in non-therm...
Jacobian Elliptic Function Method and Solitary Wave Solutions for Hybrid Lattice Equation
Institute of Scientific and Technical Information of China (English)
WANG Rui-Min; DAI Chao-Qing; ZHANG Jie-Fang
2006-01-01
In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence,twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained.When the modulus m → 1 or 0, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively.
Two-soliton interaction as an elementary act of soliton turbulence in integrable systems
Energy Technology Data Exchange (ETDEWEB)
Pelinovsky, E.N. [Department of Information Systems, National Research University – Higher School of Economics, Nizhny Novgorod (Russian Federation); Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Shurgalina, E.G.; Sergeeva, A.V.; Talipova, T.G. [Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Department of Applied Mathematics, Nizhny Novgorod State Technical University, Nizhny Novgorod (Russian Federation); El, G.A., E-mail: g.el@lboro.ac.uk [Department of Mathematical Sciences, Loughborough University (United Kingdom); Grimshaw, R.H.J. [Department of Mathematical Sciences, Loughborough University (United Kingdom)
2013-01-03
Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg–de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence.
SQUID metamaterials on a Lieb lattice: From flat-band to nonlinear localization
Lazarides, N.; Tsironis, G. P.
2017-08-01
The dynamic equations for the fluxes through the superconducting quantum interference devices (SQUIDs) that form a two-dimensional metamaterial on a Lieb lattice are derived and then linearized around zero flux to obtain the linear frequency spectrum according to the standard procedure. That spectrum due to the Lieb lattice geometry possesses a frequency band structure exhibiting two characteristic features: two dispersive bands, which form a Dirac cone at the corners of the first Brillouin zone and a flat band crossing the Dirac points. It is demonstrated numerically that localized states can be excited in the system when it is initialized with single-site excitations; depending on the amplitude of those initial states, the localization is either due to the flat-band or to nonlinear effects. Flat-band localized states are formed in the nearly linear regime, whereas localized excitations of the discrete breather type are formed in the nonlinear regime. These two regimes are separated by an intermediate turbulent regime for which no localization is observed. Notably, initial single-site excitations of only edge SQUIDs of a unit cell may end up in flat-band localized states; no such states are formed for initial single-site excitations of a corner SQUID of a unit cell. The degree of localization of the resulting states is in any case quantified using well-established measures, such as the energetic participation ratio and the second moment.
Xia, Ya-Rong; Xin, Xiang-Peng; Zhang, Shun-Li
2017-01-01
This paper mainly discusses the (2+1)-dimensional modified dispersive water-wave (MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlevé analysis and consistent tanh-function expansion (CTE) method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved. Supported by National Natural Science Foundation of China under Grant Nos. 11371293, 11505090, the Natural Science Foundation of Shaanxi Province under Grant No. 2014JM2-1009, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009 and the Science and Technology Innovation Foundation of Xi’an under Grant No. CYX1531WL41
DEFF Research Database (Denmark)
Bache, Morten; Guo, Hairun; Zhou, Binbin
2013-01-01
of the promising crystals: in one case soliton pulse compression from 50 fs to 15 fs (1.5 cycles) at 3.0 μm is achieved, and at the same time a 3-cycle dispersive wave at 5.0 μm is formed that can be isolated using a long-pass filter. In another example we show that extremely broadband supercontinua can form......We discuss a novel method for generating octave-spanning supercontinua and few-cycle pulses in the important mid-IR wavelength range. The technique relies on strongly phase-mismatched cascaded second-harmonic generation (SHG) in mid-IR nonlinear frequency conversion crystals. Importantly we here...
Dissipative surface solitons in periodic structures
Kartashov, Yaroslav V; Vysloukh, Victor A
2010-01-01
We report dissipative surface solitons forming at the interface between a semi-infinite lattice and a homogeneous Kerr medium. The solitons exist due to balance between amplification in the near-surface lattice channel and two-photon absorption. The stable dissipative surface solitons exist in both focusing and defocusing media, when propagation constants of corresponding states fall into a total semi-infinite and or into one of total finite gaps of the spectrum (i.e. in a domain where propagation of linear waves is inhibited for the both media). In a general situation, the surface solitons form when amplification coefficient exceeds threshold value. When a soliton is formed in a total finite gap there exists also the upper limit for the linear gain.
Nonlinear Photonics and Novel Optical Phenomena
Morandotti, Roberto
2012-01-01
Nonlinear Photonics and Novel Optical Phenomena contains contributed chapters from leading experts in nonlinear optics and photonics, and provides a comprehensive survey of fundamental concepts as well as hot topics in current research on nonlinear optical waves and related novel phenomena. The book covers self-accelerating airy beams, integrated photonics based on high index doped-silica glass, linear and nonlinear spatial beam dynamics in photonic lattices and waveguide arrays, polariton solitons and localized structures in semiconductor microcavities, terahertz waves, and other novel phenomena in different nanophotonic and optical systems.
Stability of solitons in PT-symmetric couplers
Driben, Rodislav
2011-01-01
Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").
Stable rotating dipole solitons in nonlocal optical media
DEFF Research Database (Denmark)
Lopez-Aguayo, Servando; Desyatnikov, Anton S.; Kivshar, Yuri S.
2006-01-01
We reveal that nonlocality can provide a simplæe physical mechanism for stabilization of multihump optical solitons and present what we believe to be the first example of stable rotating dipole solitons and soliton spiraling, which we are known to be unstable in all types of realistic nonlinear...
The soliton properties of dipole domains in superlattices
Institute of Scientific and Technical Information of China (English)
张启义; 田强
2002-01-01
The formation and propagation of dipole domains in superlattices are studied both by the modified discrete driftmodel and by the nonlinear Schrodinger equation. The spatiotemporal distribution of the electric field and electrondensity are presented. The numerical results are compared with the soliton solutions of the nonlinear Schrodingerequation and analysed. It is shown that the numerical solutions agree with the soliton solutions of the nonlinearSchrodinger equation. The dipole electric-field domains in semiconductor superlattices have the properties of solitons.
Energy Technology Data Exchange (ETDEWEB)
Yang, Jin-Wei; Gao, Yi-Tian, E-mail: gaoyt163@163.com; Wang, Qi-Min; Su, Chuan-Qi; Feng, Yu-Jie; Yu, Xin
2016-01-15
In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple–dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.
Davidson, Ronald C
2015-01-01
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius $r_{w}$. The average axial electric field is expressed as $\\langle E_{z}\\rangle=-(\\partial/\\partial z)\\langle\\phi\\rangle=-e_{b}g_{0}\\partial\\lambda_{b}/\\partial z-e_{b}g_{2}r_{w}^{2}\\partial^{3}\\lambda_{b}/\\partial z^{3}$, where $g_{0}$ and $g_{2}$ are constant geometric factors, $\\lambda_{b}(z,t)=\\int dp_{z}F_{b}(z,p_{z},t)$ is the line density of beam particles, and $F_{b}(z,p_{z},t)$ satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (solitons) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (a) the nonlinear waterbag distribution, w...
Soliton interaction in quadratic and cubic bulk media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole
2000-01-01
in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...
Ganesh, R.; Gonella, S.
2017-02-01
The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary functionalities and design adaptive spatial wave manipulators. The underlying assumption is that the magnitude of wave propagation is small with respect to the length scale of the structure under consideration, albeit large enough to elicit the effects of finite deformation. We demonstrate that the interplay of dispersion, nonlinearity and modal complexity involved in the generation and propagation of higher harmonics gives rise to secondary wave packets that feature multiple characteristics, one of which conforms to the dispersion relation of the corresponding linear structure. This provides an opportunity to engineer desired wave characteristics through a geometric and topological design of the unit cell, and results in the ability to activate complementary functionalities, typical of high frequency regimes, while operating at low frequencies of excitation - an effect seldom observed in linear periodic structures. The ability to design adaptive switches is demonstrated here using lattice configurations whose response is characterized by geometric and/or material nonlinearities.
Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling
Kartashov, Yaroslav V; Konotop, Vladimir V; Lobanov, Valery E; Torner, Lluis
2015-01-01
We introduce a mechanism to stabilize spatiotemporal solitons in Kerr nonlinear media, based on the dispersion of linear coupling between the field components forming the soliton states. Specifically, we consider solitons in a two-core guiding structure with inter-core coupling dispersion (CD). We show that CD profoundly affects properties of the solitons, causing the complete stabilization of the otherwise highly unstable spatiotemporal solitons in Kerr media with focusing nonlinearity. We also find that the presence of CD stimulates the formation of bound states, which however are unstable.
The nonlinear Schroedinger equation on a disordered chain
Energy Technology Data Exchange (ETDEWEB)
Scharf, R.; Bishop, A.R.
1990-01-01
The integrable lattice nonlinear Schroedinger equation is a unique model with which to investigate the effects of disorder on a discrete integrable dynamics, and its interplay with nonlinearity. We first review some features of the lattice nonlinear Schroedinger equation in the absence of disorder and introduce a 1- and 2-soliton collective variable approximation. Then we describe the effect of different types of disorder: attractive and repulsive isolated impurities, spatially periodic potentials, random potentials, and time dependent (kicked) long wavelength perturbations. 18 refs., 15 figs.
Soliton solutions of a generalized discrete KdV equation
Kanki, Masataka; Tokihiro, Tetsuji
2012-01-01
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This phenomenon is intuitively understood from its ultradiscrete limit, where the system turns to the box ball system with a carrier. KEYWORDS: soliton, integrable equation, nonlinear system, discrete KdV equation, cellular automaton
Observation of Dissipative Bright Soliton and Dark Soliton in an All-Normal Dispersion Fiber Laser
Directory of Open Access Journals (Sweden)
Chunyang Ma
2016-01-01
Full Text Available This paper proposes a novel way for controlling the generation of the dissipative bright soliton and dark soliton operation of lasers. We observe the generation of dissipative bright and dark soliton in an all-normal dispersion fiber laser by employing the nonlinear polarization rotation (NPR technique. Through adjusting the angle of the polarizer and analyzer, the mode-locked and non-mode-locked regions can be obtained in different polarization directions. Numerical simulation shows that, in an appropriate pump power range, the dissipative bright soliton and dark soliton can be generated simultaneously in the mode-locked and non-mode-locked regions, respectively. If the pump power exceeds the top limit of this range, only dissipative soliton will exist, whereas if it is below the lower bound of this range, only dark soliton will exist.
Soliton coding for secured optical communication link
Amiri, Iraj Sadegh; Idrus, Sevia Mahdaliza
2015-01-01
Nonlinear behavior of light such as chaos can be observed during propagation of a laser beam inside the microring resonator (MRR) systems. This Brief highlights the design of a system of MRRs to generate a series of logic codes. An optical soliton is used to generate an entangled photon. The ultra-short soliton pulses provide the required communication signals to generate a pair of polarization entangled photons required for quantum keys. In the frequency domain, MRRs can be used to generate optical millimetre-wave solitons with a broadband frequency of 0?100 GHz. The soliton signals are multi
Nonlinear endoscopy with Kagomé lattice hollow-core fibers (Conference Presentation)
Lombardini, Alberto; Sivankutty, Siddharth; Chen, Xueqin; Wenger, Jérôme; Habert, Rémi; Fourcade-Dutin, Coralie; Andresen, Esben R.; Kudlinski, Alexandre; Rigneault, Hervé
2016-03-01
The development of nonlinear fiber-endoscopes capable of imaging deeper in tissues and accessing internal organs represents a very attractive perspective for application of nonlinear optical microscopes to in-vivo research and diagnostics. The transmission of ultra-short laser pulses within a fiber is a critical issue in the development of such endoscopes. For instance, self-phase modulation (SPM), four-wave mixing (FWM) and Raman scattering occurring in conventional fibers severely affect transmitted pulses profiles in the time and frequency domains. Hollow-core (HC) fibers bring a solution to the problem, since propagation of the pulses in the air core limits nonlinear interactions. We employ here a novel double clad Kagomé-lattice HC fiber for the delivery of ultrafast pulses across a large spectral window (~400nm) with no pulse distortion. The epi-collection of the signal generated at the sample is efficiently performed with a specially designed outer multimode cladding. The fiber is incorporated in a prototype endoscope using a four-quartered piezo-electric tube to scan the laser beam on the sample. The low numerical aperture of the hollow-core (0.02) is efficiently increased by means of a dielectric microsphere attached to the fiber face. This results in tight focusing (~1 micron) of the beam at the HC fiber output. Resonant scanning of the fiber tip allows imaging over a field of 300 microns using low driving voltages. High-resolution images with different contrast mechanisms, such as SHG and TPEF, acquired with the prototype endoscope illustrate the potential of these fibers for nonlinear imaging in regions otherwise inaccessible to conventional optical microscopes.
A Simple Method to Obtain Exact Soliton Solutions for a Nonlinear Equation in a Loss Fibre System
Institute of Scientific and Technical Information of China (English)
YANGXiao－Xue; WUYing; 等
2002-01-01
We show that the nonlinear equation governing wave propagation in a loss fibre system considered by Nakkerian in J.Phys.A34(2001) 5111 can be brought into the standard nonlinear schroedinger equation by a simple transformation.
Generalized sine-Gordon solitons
Energy Technology Data Exchange (ETDEWEB)
Santos, C dos [Centro de Fisica e Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, 4169-007 Porto (Portugal); Rubiera-Garcia, D, E-mail: cssilva@fc.up.pt, E-mail: rubieradiego@gmail.com [Departamento de Fisica, Universidad de Oviedo, Avenida Calvo Sotelo 18, 33007 Oviedo, Asturias (Spain)
2011-10-21
In this paper, we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we use a projection method applied to the sine-Gordon soliton. We focus our attention on the wall and lump-like soliton solutions of these k-field models. These solutions and their potentials reduce to those of the Klein-Gordon kink and the standard lump for the case of a canonical kinetic term. As we increase the nonlinearity on the kinetic term the corresponding potentials get modified and the nature of the soliton may change, in particular, undergoing a topology modification. The procedure constructed here is shown to be a sort of generalization of the deformation method for a specific class of k-field models. (paper)
The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation
Dong, Huanhe; Zhang, Yong; Zhang, Xiaoen
2016-07-01
A discrete matrix spectral problem is presented and the hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established. As to the discrete integrable system, nonlinearization of the spatial parts of the Lax pairs and the adjoint Lax pairs generate a new integrable symplectic map. Based on the theory, a new integrable symplectic map and a family of finite-dimension completely integrable systems are given. Especially, two explicit equations are obtained under the Bargmann constraint. Finally, the symmetry of the discrete equation is provided according to the recursion operator and the seed symmetry. Although the solutions of the discrete equations have been gained by many methods, there are few articles that solving the discrete equation via the symmetry. So the solution of the discrete lattice equation is obtained through the symmetry theory.
Regularized degenerate multi-solitons
Correa, Francisco
2016-01-01
We report complex PT-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schroedinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota's direct method or on a nonlinear superposition obtained from multiple Baecklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.
Nonlinear nano-scale localized breather modes in a discrete weak ferromagnetic spin lattice
Energy Technology Data Exchange (ETDEWEB)
Kavitha, L., E-mail: louiskavitha@yahoo.co.in [Department of Physics, School of Basic and Applied Sciences, Central University of Tamil Nadu (CUTN), Thiruvarur 610 101, Tamil Nadu (India); Max-Planck Institute for the Physics of Complex Systems, Dresden (Germany); The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Parasuraman, E. [Department of Physics, Periyar University, Salem 636 011, Tamil Nadu (India); Center for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, Tamil Nadu (India); Gopi, D. [Department of Chemistry, Periyar University, Salem 636 011, Tamil Nadu (India); Center for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, Tamil Nadu (India); Prabhu, A. [Department of Physics, Periyar University, Salem 636 011, Tamil Nadu (India); Vicencio, Rodrigo A. [Departamento de Física and MSI-Nucleus on Advanced Optics, Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago 7800003 (Chile); Max-Planck Institute for the Physics of Complex Systems, Dresden (Germany)
2016-03-01
We investigate the propagation dynamics of highly localized discrete breather modes in a weak ferromagnetic spin lattice with on-site easy axis anisotropy due to crystal field effect. We derive the discrete nonlinear equation of motion by employing boson mappings and p-representation. We explore the onset of modulational instability both analytically in the framework of linear stability analysis and numerically by means of molecular dynamics (MD) simulations, and a perfect agreement was demonstrated. It is also explored that how the antisymmetric nature of the canted ferromagnetic lattice supports highly localized discrete breather (DBs) modes as shown in the stability/instability windows. The energy exchange between low amplitude discrete breathers favours the growth of higher amplitude DBs, resulting eventually in the formation of few long-lived high amplitude DBs. - Highlights: • The effects of DM and anisotropy interaction on the DB modes are studied. • The antisymmetric nature of the canted ferromagnetic medium supports the DB modes. • Dynamics of ferromagnetic chain is governed by boson mappings and p-representation.
Institute of Scientific and Technical Information of China (English)
JI Jie
2008-01-01
In this paper, we present an extended Exp-function method to differential-difference equation(s). With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.
Institute of Scientific and Technical Information of China (English)
Song Wei
2009-01-01
We have investigated the intrinsic decoherence on the entanglement of a two-qutrit one-dimensional (1D) optical lattice chain with nonlinear coupling.As a measure of the entanglement,the negativity of the system is calculated.It is shown that the influence of intrinsic decoherence on the entanglement varies in different initial systems.
Veldes, G P; Cuevas, J; Kevrekidis, P G; Frantzeskakis, D J
2013-07-01
We study the coupling between backward- and forward-propagating wave modes, with the same group velocity, in a composite right- and left-handed nonlinear transmission line. Using an asymptotic multiscale expansion technique, we derive a system of two coupled nonlinear Schrödinger equations governing the evolution of the envelopes of these modes. We show that this system supports a variety of backward- and forward-propagating vector solitons of the bright-bright, bright-dark, and dark-bright type. Performing systematic numerical simulations in the framework of the original lattice that models the transmission line, we study the propagation properties of the derived vector soliton solutions. We show that all types of the predicted solitons exist, but differ on their robustness: Only bright-bright solitons propagate undistorted for long times, while the other types are less robust, featuring shorter lifetimes. In all cases, our analytical predictions are in very good agreement with the results of the simulations, at least up to times of the order of the solitons' lifetimes.
Zhou, B B; Bache, M
2014-01-01
Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO$_3$ cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband ($\\sim 1,000$ cm$^{-1}$) mid-IR pulses around $3.0~\\mu\\rm m$ are generated with excellent spatio-temporal pulse quality, having up to 10.5 $\\mu$J energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily by using large-aperture crystals. The technique can readily be implemented with other crystals and la...
Compression limits in cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw;
2008-01-01
Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency.......Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency....
Cascaded quadratic soliton compression at 800 nm
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey;
2007-01-01
We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion.......We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
Bragg Fibers with Soliton-like Grating Profiles
Directory of Open Access Journals (Sweden)
Bugaychuk S.
2016-01-01
Full Text Available Nonlinear dynamical system corresponding to the optical holography in a nonlocal nonlinear medium with dissipation contains stable localized spatio-temporal states, namely the grid dissipative solitons. These solitons display a non-uniform profile of the grating amplitude, which has the form of the dark soliton in the reflection geometry. The transformation of the grating amplitude gives rise many new atypical effects for the beams diffracted on such grating, and they are very suitable for the fiber Brass gratings. The damped nonlinear Schrodinger equation is derived that describes the properties of the grid dissipative soliton.
Parametric localized modes in quadratic nonlinear photonic structures
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;
2001-01-01
We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....
Voronin, A. A.; Zheltikov, A. M.
2017-02-01
Analysis of the group-velocity dispersion (GVD) of atmospheric air with a model that includes the entire manifold of infrared transitions in air reveals a remarkably broad and continuous anomalous-GVD region in the high-frequency wing of the carbon dioxide rovibrational band from approximately 3.5 to 4.2 μm where atmospheric air is still highly transparent and where high-peak-power sources of ultrashort midinfrared pulses are available. Within this range, anomalous dispersion acting jointly with optical nonlinearity of atmospheric air is shown to give rise to a unique three-dimensional dynamics with well-resolved soliton features in the time domain, enabling a highly efficient whole-beam soliton self-compression of such pulses to few-cycle pulse widths.
Single-mode dispersive waves and soliton microcomb dynamics
Yi, Xu; Yang, Qi-Fan; Zhang, Xueyue; Yang, Ki Youl; Li, Xinbai; Vahala, Kerry
2017-03-01
Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications.
Institute of Scientific and Technical Information of China (English)
刘煜
2009-01-01
According to the characteristics of peaked soliton solution, the undetermined coefficient method for solving nonlinear wave equations for their peaked soliton solutions is submitted and by means of the method several kinds of peaked soliton solutions are obtained for five nonlinear wave equations: the Camassa-Holm, fifth-order KdV-like, generalized Ostrovsky, combined KdV-mKdV and Klein-Gordon equations. The solutions given in literature about Camassa-Holm equation become the special cases of the solutions in this paper. The graphs of some solutions are given through numerical simulation. The special conditions under which the wave equation will have peaked soliton solution is briefly described. The method used in this paper can also be used for solving many other nonlinear equations.%根据尖峰孤子解的特点,提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法,并利用该方法求解了5个非线性波方程,即CH(Camassa-Holm)方程、五阶KdV-like方程、广义Ostrovskv方程、组合KdV-mKdV方程和Klein-Gordon方程,比较简便地得到了这些方程的尖峰孤子解.文献中关于CH方程的结果成为本文结果的特例.通过数值模拟给出了部分解的图像.简要说明了非线性波方程存在尖峰孤子解所须满足的特定条件.该方法也适用于求其他非线性波方程的尖峰孤子解.
Olsen, M.; Smith, H.; Scott, A. C.
1984-09-01
A wave tank experiment (first described by the nineteenth-century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment is intended for lecture demonstrations.
Langmuir Solitons in Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Mjølhus, E.; Pécseli, Hans;
1978-01-01
The authors have considered the nonlinear interaction between a high frequency (Langmuir) wave, which propagates at an arbitrary angle to a weak, constant magnetic field, and low frequency (ion-cyclotron or ion-sound) perturbations. In studying Langmuir envelope solitons they have unified...
DEFF Research Database (Denmark)
Olsen, M.; Smith, H.; Scott, Alwyn C.
1984-01-01
A wave tank experiment (first described by the nineteenth-century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment...
Control of soliton characteristics of the condensate by an arbitrary x-dependent external potential
Institute of Scientific and Technical Information of China (English)
Yang Ru-Shu; Yao Chun-Mei; Chen Ri-Xin
2009-01-01
This paper presents a family of soliton solutions of the one-dimensional nonlinear Schrodinger equation which describes the dynamics of the dark solitons in Bose-Einstein condensates with an arbitrary x-dependent external potential. The obtained results show that the external potential has an important effect on the dark soliton dynamical characteristics of the condensates. The amplitude,width,and velocity of the output soliton are relative to the source position of the external potential. The smaller the amplitude of the soliton is,the narrower its width is,and the slower the soliton propagates. The collision of two dark solitons is nearly elastic.
Optical Spatial Solitons and Their Interactions: Universality and Diversity.
Stegeman; Segev
1999-11-19
Spatial solitons, beams that do not spread owing to diffraction when they propagate, have been demonstrated to exist by virtue of a variety of nonlinear self-trapping mechanisms. Despite the diversity of these mechanisms, many of the features of soliton interactions and collisions are universal. Spatial solitons exhibit a richness of phenomena not found with temporal solitons in fibers, including effects such as fusion, fission, annihilation, and stable orbiting in three dimensions. Here the current state of knowledge on spatial soliton interactions is reviewed.
Propagation of an Airy-Gaussian beam in defected photonic lattices
Shi, Zhiwei; Zhu, Xing; Li, Yang; Li, Huagang
2016-01-01
We investigate numerically that a finite Airy-Gaussian (AiG) beam varies its trajectory and shape in the defected photonic lattices. The propagation properties and beam self-bending are controlled with modulation depth and period of the photonic lattices, positive and negative defects, beam distribution factor and nonlinearity change. For positive defects, the pseudo-period oscillation and localization of the AiG beam may be formed under a certain condition, while the beam is diffused for negative defects. Moreover, the solitons may appear during the propagation process when the self-focusing nonlinearity is introduced.
3D simulation for solitons used in optical fibers
Vasile, F.; Tebeica, C. M.; Schiopu, P.; Vladescu, M.
2016-12-01
In this paper is described 3D simulation for solitions used in optical fibers. In the scientific works is started from nonlinear propagation equation and the solitons represents its solutions. This paper presents the simulation of the fundamental soliton in 3D together with simulation of the second order soliton in 3D. These simulations help in the study of the optical fibers for long distances and in the interactions between the solitons. This study helps the understanding of the nonlinear propagation equation and for nonlinear waves. These 3D simulations are obtained using MATLAB programming language, and we can observe fundamental difference between the soliton and the second order/higher order soliton and in their evolution.
A new non-linear vortex lattice method:Applications to wing aerodynamic optimizations
Institute of Scientific and Technical Information of China (English)
Oliviu S? ugar Gabor; Andreea Koreanschi; Ruxandra Mihaela Botez
2016-01-01
This paper presents a new non-linear formulation of the classical Vortex Lattice Method (VLM) approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.
Topology Dependence in Lattice Simulations of Non-Linear Pdes on a Mimd Computer
Valin, P.; Goulard, B.; Sanielevici, M.
We tested the parallelization of explicit schemes for the solution of non-linear classical field theories of complex scalar fields which are capable of simulating hadronic collisions. Our attention focused on collisions in a fractional model with a particularly rich inelastic spectrum of final states. Relativistic collisions of all types were performed by computer on large lattices (64 to 256 sites per dimension). The stability and accuracy of the objects were tested by the use of two other methods of solutions: Pseudo-spectral and semi-implicit. Parallelization of the Fortran code on a 64-transputer MIMD Volvox machine revealed, for certain topologies, communication deadlock and less-than-optimum routing strategies when the number of transputers used was less than the maximum. The observed speedup, for N transputers in an appropriate topology, is shown to scale approximately as N, but the overall gain in execution speed, for physically interesting problems, is a modest 2-3 when compared to state-of-the-art workstations.
A new non-linear vortex lattice method: Applications to wing aerodynamic optimizations
Directory of Open Access Journals (Sweden)
Oliviu Şugar Gabor
2016-10-01
Full Text Available This paper presents a new non-linear formulation of the classical Vortex Lattice Method (VLM approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.
Optical analogue of relativistic Dirac solitons in binary waveguide arrays
Energy Technology Data Exchange (ETDEWEB)
Tran, Truong X., E-mail: truong.tran@mpl.mpg.de [Department of Physics, Le Quy Don University, 236 Hoang Quoc Viet str., 10000 Hanoi (Viet Nam); Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); Longhi, Stefano [Department of Physics, Politecnico di Milano and Istituto di Fotonica e Nanotecnologie del Consiglio Nazionale delle Ricerche, Piazza L. da Vinci 32, I-20133 Milano (Italy); Biancalana, Fabio [Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); School of Engineering and Physical Sciences, Heriot-Watt University, EH14 4AS Edinburgh (United Kingdom)
2014-01-15
We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An optical analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.
Generalized Theory of One-Dimensional Steady-State Optical Spatial Solitons
Institute of Scientific and Technical Information of China (English)
WANG Hong-Cheng; WANG Xiao-Sheng; SHE Wei-Long
2004-01-01
@@ We present a generalized soliton theory based on the one-dimensional generalized nonlinear Schrodinger equation,from which one can easily obtain the bright, dark, and grey soliton waveforms, and their existence curves. We show that the forming conditions of spatial solitons are directly dependent on the relationship between the index perturbation and the intensity, no matter whether the index perturbation is positive or negative. Some relevant examples are presented when the solitons are supported by the photoisomerization nonlinearity.
Institute of Scientific and Technical Information of China (English)
王学文; 王华兰; 王成
2009-01-01
A family of higher-order solitons called elegant Hermite Gaussian higher-order soliton (EHGHOS) in the strongly nonlocal nonlinear media is introduced.The transverse distribution of EHGHOS at the entrance plane is the same as the waist of elegant Hermite Gaussian beam.And it presents as periodical evolution with the period Δz=π/β0when propagates.%本文得到了强非局域非线性介质中的一类高阶空间孤子,即完美厄米高斯高阶孤子.此类高阶孤子在入射面处的场分布与完美厄米高斯光束束腰处的场分布相同.在传输过程中,其场分布呈周期性演化,周期为Δz=π/β0.
Staggered and short period solutions of the Saturable Discrete Nonlinear Schr\\"odinger Equation
Khare, Avinash; Samuelsen, Mogens R; Saxena, Avadh; 10.1088/1751-8113/42/8/085002
2010-01-01
We point out that the nonlinear Schr{\\"o}dinger lattice with a saturable nonlinearity also admits staggered periodic as well as localized pulse-like solutions. Further, the same model also admits solutions with a short period. We examine the stability of these solutions and find that the staggered as well as the short period solutions are stable in most cases. We also show that the effective Peierls-Nabarro barrier for the pulse-like soliton solutions is zero.
Van Gorder, Robert A.
2016-05-01
Very recent experimental work has demonstrated the existence of Kelvin waves along quantized vortex filaments in superfluid helium. The possible configurations and motions of such filaments is of great physical interest, and Svistunov previously obtained a Hamiltonian formulation for the dynamics of quantum vortex filaments in the low-temperature limit under the assumption that the vortex filament is essentially aligned along one axis, resulting in a two-dimensional (2D) problem. It is standard to approximate the dynamics of thin filaments by employing the local induction approximation (LIA), and we show that by putting the two-dimensional LIA into correspondence with the first equation in the integrable Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy, we immediately obtain solutions to the two-dimensional LIA, such as helix, planar, and self-similar solutions. These solutions are obtained in a rather direct manner from the WKIS equation and then mapped into the 2D-LIA framework. Furthermore, the approach can be coupled to existing inverse scattering transform results from the literature in order to obtain solitary wave solutions including the analog of the Hasimoto one-soliton for the 2D-LIA. One large benefit of the approach is that the correspondence between the 2D-LIA and the WKIS allows us to systematically obtain vortex filament solutions directly in the Cartesian coordinate frame without the need to solve back from curvature and torsion. Implications of the results for the physics of experimentally studied solitary waves, Kelvin waves, and postvortex reconnection events are mentioned.
Williams, G. Jackson; Lee, Sooheyong; Walko, Donald A.; Watson, Michael A.; Jo, Wonhuyk; Lee, Dong Ryeol; Landahl, Eric C.
2016-12-01
Nonlinear optical phenomena in semiconductors present several fundamental problems in modern optics that are of great importance for the development of optoelectronic devices. In particular, the details of photo-induced lattice dynamics at early time-scales prior to carrier recombination remain poorly understood. We demonstrate the first integrated measurements of both optical and structural, material-dependent quantities while also inferring the bulk impulsive strain profile by using high spatial-resolution time-resolved x-ray scattering (TRXS) on bulk crystalline gallium arsenide. Our findings reveal distinctive laser-fluence dependent crystal lattice responses, which are not described by previous TRXS experiments or models. The initial linear expansion of the crystal upon laser excitation stagnates at a laser fluence corresponding to the saturation of the free carrier density before resuming expansion in a third regime at higher fluences where two-photon absorption becomes dominant. Our interpretations of the lattice dynamics as nonlinear optical effects are confirmed by numerical simulations and by additional measurements in an n-type semiconductor that allows higher-order nonlinear optical processes to be directly observed as modulations of x-ray diffraction lineshapes.
Kalashnikov, Vladimir L
2010-01-01
The analytical theory of chirped dissipative soliton solutions of nonlinear complex Ginzburg-Landau equation is exposed. Obtained approximate solutions are easily traceable within an extremely broad range of the equation parameters and allow a clear physical interpretation as a representation of the strongly chirped pulses in mode-locked both solid-state and fiber oscillators. Scaling properties of such pulses demonstrate a feasibility of sub-mJ pulse generation in the continuous-wave mode-locking regime directly from an oscillator operating at the MHz repetition rate.
Stable helical solitons in optical media
Indian Academy of Sciences (India)
Boris Malomed; G D Peng; P L Chu; Isaac Towers; Alexander V Buryak; Rowland A Sammut
2001-11-01
We present a review of new results which suggest the existence of fully stable spinning solitons (self-supporting localised objects with an internal vorticity) in optical ﬁbres with self-focusing Kerr (cubic) nonlinearity, and in bulk media featuring a combination of the cubic self-defocusing and quadratic nonlinearities. Their distinctive difference from other optical solitons with an internal vorticity, which were recently studied in various optical media, theoretically and also experimentally, is that all the spinning solitons considered thus far have been found to be unstable against azimuthal perturbations. In the ﬁrst part of the paper, we consider solitons in a nonlinear optical ﬁbre in a region of parameters where the ﬁbre carries exactly two distinct modes, viz., the fundamental one and the ﬁrst-order helical mode. From the viewpoint of application to communication systems, this opens the way to doubling the number of channels carried by a ﬁbre. Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical ﬁbres. We introduce a system of coupled nonlinear Schrödinger equations for the fundamental and helical modes with nonstandard values of the cross-phase-modulation coupling constants, and show, in analytical and numerical forms, results of collisions between solitons carried by the two modes. In the second part of the paper, we demonstrate that the interaction of the fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing Kerr nonlinearity, gives rise to the ﬁrst ever example of completely stable spatial ring-shaped solitons with intrinsic vorticity. The stability is demonstrated both by direct simulations and by analysis of linearized equations.
Soliton models in resonant and nonresonant optical ﬁbers
Indian Academy of Sciences (India)
K Porsezian
2001-11-01
In this review, considering the important linear and nonlinear optical effects like group velocity dispersion, higher order dispersion, Kerr nonlinearity, self-steepening, stimulated Raman scattering, birefringence, self-induced transparency and various inhomogeneous effects in ﬁbers, the completely integrable concept and bright, dark and self-induced transparency soliton models in nonlinear ﬁber optics are discussed. Considering the above important optical effects, the different completely integrable soliton models in the form of nonlinear Schrödinger (NLS), NLS-MaxwellBloch (MB) type equations reported in the literature are discussed. Finally, solitons in stimulated Raman scattering (SRS) system is brieﬂy discussed.
Gunasekaran, Sharmila; Kunduri, Hari K
2016-01-01
The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have non-zero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This `first law of black hole and soliton mechanics' contains new intensive and extensive quantities associated to each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulae relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.
Gunasekaran, Sharmila; Hussain, Uzair; Kunduri, Hari K.
2016-12-01
The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess nontrivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have nonzero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This "first law of black hole and soliton mechanics" contains new intensive and extensive quantities associated with each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulas relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.
Symmetry breaking of solitons in two-dimensional complex potentials
Yang, Jianke
2014-01-01
Symmetry breaking is reported for continuous families of solitons in the nonlinear Schr\\"odinger equation with a two-dimensional complex potential. This symmetry-breaking bifurcation is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, such symmetry breaking is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base branch of symmetry-unbroken solitons. Stability of these solitons near the bifurcation point are also studied, and two novel stability properties for the bifurcated asymmetric solitons are revealed. One is that at the bifurcation point, zero and simple imaginary linear-stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability. The other is that the two bifurcated asymmetric solitons, even though having identical powers and being related to each other by spatial mirror reflection, can possess different types of unstable eigenval...
Breathing dissipative solitons in optical microresonators
Lucas, Erwan; Guo, Hairun; Gorodetsky, Michael; Kippenberg, Tobias
2016-01-01
Dissipative solitons are self-localized structures resulting from a double balance between dispersion and nonlinearity as well as dissipation and a driving force. They occur in a wide variety of fields ranging from optics, hydrodynamics to chemistry and biology. Recently, significant interest has focused on their temporal realization in driven optical microresonators, known as dissipative Kerr solitons. They provide access to coherent, chip-scale optical frequency combs, which have already been employed in optical metrology, data communication and spectroscopy. Such Kerr resonator systems can exhibit numerous localized intracavity patterns and provide rich insights into nonlinear dynamics. A particular class of solutions consists of breathing dissipative solitons, representing pulses with oscillating amplitude and duration, for which no comprehensive understanding has been presented to date. Here, we observe and study single and multiple breathing dissipative solitons in two different microresonator platforms...
Discrete solitons in coupled active lasing cavities
Prilepsky, Jaroslaw E; Johansson, Magnus; Derevyanko, Stanislav A
2012-01-01
We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active media, where the gain exceeds damping in the linear limit. A zoo of stable localized structures is found and classified: these are bright and grey cavity solitons with different symmetry. It is shown that several new types of solitons with a nontrivial intensity distribution pattern can emerge in the coupled cavities due to the stability of a periodic extended state. The latter can be stable even when a bistability of homogenous states is absent.
Dark solitons in mode-locked lasers
Ablowitz, Mark J; Nixon, Sean D; Frantzeskakis, Dimitri J
2010-01-01
Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model which incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions evolve into dark solitons under appropriate requirements also met in the experimental observations. The resulting pulses are well approximated by dark solitons of the unperturbed nonlinear Schr\\"{o}dinger equation. Notably, the same framework also describes bright pulses in anomalous and normally dispersive lasers.
Stable surface solitons in truncated complex potentials.
He, Yingji; Mihalache, Dumitru; Zhu, Xing; Guo, Lina; Kartashov, Yaroslav V
2012-07-01
We show that surface solitons in the one-dimensional nonlinear Schrödinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of the surface solitons shrink with an increase in the amplitude of the imaginary part of complex potential.
Stable surface solitons in truncated complex potentials
He, Yingji; Zhu, Xing; Guo, Lina; Kartashov, Yaroslav V
2012-01-01
We show that surface solitons in the one-dimensional nonlinear Schr\\"odinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of surface solitons shrink with increase of the amplitude of imaginary part of complex potential.
Zayed, Elsayed M. E.; Al-Nowehy, Abdul-Ghani; Elshater, Mona E. M.
2017-06-01
The (G^'/G)-expansion method, the improved Sub-ODE method, the extended auxiliary equation method, the new mapping method and the Jacobi elliptic function method are applied in this paper for finding many new exact solutions including Jacobi elliptic solutions, solitary solutions, singular solitary solutions, trigonometric function solutions and other solutions to the nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity whose balance number is not positive integer. The used methods present a wider applicability for handling the nonlinear partial differential equations. A comparison of our new results with the well-known results is made. Also, we compare our results with each other yielding from these five integration tools.
Sun, Yan; Tian, Bo; Zhen, Hui-Ling; Wu, Xiao-Yu; Xie, Xi-Yang
2016-07-01
Under investigation in this paper is a (3 + 1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation, which describes the nonlinear behaviors of ion-acoustic waves in a magnetized plasma where the cooler ions are treated as a fluid with adiabatic pressure and the hot isothermal electrons are described by a Boltzmann distribution. With the Hirota method and symbolic computation, we obtain the one-, two- and three-soliton solutions for such an equation. We graphically study the solitons related with the coefficient of the cubic nonlinearity M. Amplitude of the one soliton increases with increasing M, but the width of one soliton keeps unchanged as M increases. The two solitons and three solitons are parallel, and the amplitudes of the solitons increase with increasing M, but the widths of the solitons are unchanged. It is shown that the interactions between the two solitons and among the three solitons are elastic.
Single-mode dispersive waves and soliton microcomb dynamics
Yi, Xu; Zhang, Xueyue; Yang, Ki Youl; Vahala, Kerry
2016-01-01
Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and to offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power in the form of a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. A limiting case is demonstrated in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton is shown to induce bistable behavior in the spectral and temporal properties of the soliton. Also, an operating point of enhanced repetition-rate stability is predicted and observed. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications.
Soliton and kink jams in traffic flow with open boundaries.
Muramatsu, M; Nagatani, T
1999-07-01
Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.
Dissipative plasmon solitons in graphene nanodisk arrays
Smirnova, Daria A; Smirnov, Lev A; Kivshar, Yuri S
2014-01-01
We study nonlinear modes in one-dimensional arrays of doped graphene nanodisks with Kerr-type nonlinear response in the presence of an external electric field. We present the theoretical model describing the evolution of the disks' polarizations, taking into account intrinsic graphene losses and dipole-dipole coupling between the graphene nanodisks. We reveal that this nonlinear system can support discrete dissipative scalar solitons of both longitudinal and transverse polarizations, as well as vector solitons composed of two mutually coupled polarization components. We demonstrate the formation of stable resting and moving localized modes under controlling guidance of the external driving field.
Wang, W. B.; Wang, F.; Yu, Q.; Zhang, X.; Lu, Y. X.; Gu, J.
2016-11-01
We propose and experimentally demonstrate a bidirectional erbium-doped fiber laser delivering dispersion-managed soliton (DMS) and Q-switched pulse based on a graphene-polyvinyl alcohol (PVA) and nonlinear optical loop mirror (NOLM) saturable absorbers (SAs). In proposed structure, the DMS is achieved in clockwise (CW) direction and Q-switched pulse is obtained in counter-clockwise (CCW) direction. By properly adjusting the intracavity attenuators (ATT) and polarizer controllers (PCs), DMS in the CW direction and Q-switched pulse in the CCW direction can be obtained, respectively or simultaneously. The DMS with full width at half maximum (FWHM) of ~480 fs, signal to noise ratio (SNR) of ~60 dB and repetition frequency about 3.907 MHz is obtained. The Q-switched pulse is established at a pump power of 180 mW with a repetition rate of ~43.5 kHz and FWHM of ~8.18 μs. When the pump power is increased to 700 mW, Q-switched pulse with a repetition rate of ~107.1 kHz and FWHM of ~2.15 μs is generated. When the two type pulses are formed simultaneously, the maximum repetition rate of Q-switched pulse is 55.8 kHz and minimum FWHM is 2.81 μs, the DMS can be formed by properly adjusting PC and ATT in this case. To the best of our knowledge, it is the first time that Q-switched pulse and DMS have been acquired respectively or simultaneously in a fiber laser.
Ghosh, Samiran
2014-09-01
The propagation of a nonlinear low-frequency mode in two-dimensional (2D) monolayer hexagonal dusty plasma crystal in presence of external magnetic field and dust-neutral collision is investigated. The standard perturbative approach leads to a 2D Korteweg-de Vries (KdV) soliton for the well-known dust-lattice mode. However, the Coriolis force due to crystal rotation and Lorentz force due to magnetic field on dust particles introduce a linear forcing term, whereas dust-neutral drag introduce the usual damping term in the 2D KdV equation. This new nonlinear equation is solved both analytically and numerically to show the competition between the linear forcing and damping in the formation of quasilongitudinal soliton in a 2D strongly coupled complex (dusty) plasma. Numerical simulation on the basis of the typical experimental plasma parameters and the analytical solution reveal that the neutral drag force is responsible for the usual exponential decay of the soliton, whereas Coriolis and/or Lorentz force is responsible for the algebraic decay as well as the oscillating tail formation of the soliton. The results are discussed in the context of the plasma crystal experiment.
Zhao, L. M.; Bartnik, A. C.; Tai, Q. Q.; Wise, F. W.
2013-01-01
Theoretical and experimental investigations of the behavior of normal-dispersion fiber lasers with nonlinear-optical loop mirrors are presented. The use of a loop mirror causes the laser to generate relatively long, flat-topped pulses. The pulse energy can be high, but the pulse duration is limited to greater than 300 fs. Experimentally, 8-nJ pulses that can be dechirped to 340 fs duration are obtained. The laser is a step toward an all-fiber, environmentally-stable design. PMID:23722797
Qin, Bo; Tian, Bo; Wang, Yu-Feng; Shen, Yu-Jia; Wang, Ming
2017-10-01
Under investigation in this paper are the Belov-Chaltikian (BC), Leznov and Blaszak-Marciniak (BM) lattice equations, which are associated with the conformal field theory, UToda(m_1,m_2) system and r-matrix, respectively. With symbolic computation, the Bell-polynomial approach is developed to directly bilinearize those three sets of differential-difference nonlinear evolution equations (NLEEs). This Bell-polynomial approach does not rely on any dependent variable transformation, which constitutes the key step and main difficulty of the Hirota bilinear method, and thus has the advantage in the bilinearization of the differential-difference NLEEs. Based on the bilinear forms obtained, the N-soliton solutions are constructed in terms of the N × N Wronskian determinant. Graphic illustrations demonstrate that those solutions, more general than the existing results, permit some new properties, such as the solitonic propagation and interactions for the BC lattice equations, and the nonnegative dark solitons for the BM lattice equations.
Moving lattice kinks and pulses: an inverse method.
Flach, S; Zolotaryuk, Y; Kladko, K
1999-05-01
We develop a general mapping from given kink or pulse shaped traveling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping-by definition an inverse method-to acoustic solitons in chains with nonlinear intersite interactions, nonlinear Klein-Gordon chains, reaction-diffusion equations, and discrete nonlinear Schrödinger systems. Potential functions can be found in a unique way provided the pulse shape is reflection symmetric and pulse and kink shapes are at least C2 functions. For kinks we discuss the relation of our results to the problem of a Peierls-Nabarro potential and continuous symmetries. We then generalize our method to higher dimensional lattices for reaction-diffusion systems. We find that increasing also the number of components easily allows for moving solutions.
一类非线性发展方程的复合型双孤子新解∗%New complexion two-soliton solutions of a class of nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
套格图桑; 伊丽娜
2015-01-01
通过下列步骤，构造了一类非线性发展方程的无穷序列复合型双孤子新解：步骤一，给出两种函数变换，把一类非线性发展方程化为二阶非线性常微分方程；步骤二，再通过函数变换，二阶非线性常微分方程转化为一阶非线性常微分方程组，并获得了该方程组的首次积分；步骤三，利用首次积分与两种椭圆方程的新解与Bäcklund变换，构造了一类非线性发展方程的无穷序列复合型双孤子新解。%New infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation are constructed with the help of function transformations and two kinds of elliptic equations. Step one,according to two function transformations, a kind of nonlinear evolution equation is changed into a nonlinear ordinary differential equation of second order. Step two, using function transformation, the nonlinear ordinary differential equation of second order is transformed into a set of nonlinear ordinary differential equations of first order, and the first integral of the set of equations is obtained. Finally, the first integral with new solutions and Bäcklund transformation of two kinds of elliptic equations are used to search for new infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation.
Stability of Bright Solitons in Bose-Einstein Condensates
Institute of Scientific and Technical Information of China (English)
YU Hui-You; YAN Jia-Ren; XIE Qiong-Tao
2004-01-01
We investigate the stability of bright solitons in Bose-Einstein condensates by including a feeding term and a loss one in the Gross-Pitaevskii equation. Based on the direct approach of perturbation theory for the nonlinear Schrodinger equation, we give the explicit dependence of the height and other related quantities of bright solitons on the feeding and loss term. It is found that the three-body recombination loss plays a crucial role in stabilizing bright solitons.
Institute of Scientific and Technical Information of China (English)
Bai Cheng-Lin; Zhang Xia; Zhang Li-Hua
2009-01-01
This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-differenceequations (NLDDEs) and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the (2+l)-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential-difference equations.
Graphene supports the propagation of subwavelength optical solitons
Nesterov, M L; Nikitin, A Yu; Garcia-Vidal, F J; Martin-Moreno, L
2012-01-01
We study theoretically nonlinear propagation of light in a graphene monolayer. We show that the large intrinsic nonlinearity of graphene at optical frequencies enables the formation of quasi one-dimensional self-guided beams (spatial solitons) featuring subwavelength widths at moderate electric-field peak intensities. We also demonstrate a novel class of nonlinear self-confined modes resulting from the hybridization of surface plasmon polaritons with graphene optical solitons.
Soliton and similarity solutions of N=2,4 supersymmetric equations
Delisle, Laurent
2012-01-01
We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg-de Vries and modified KdV equations. We give new representations of the $\\tau$-functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.
Soliton and Similarity Solutions of Ν = 2, 4 Supersymmetric Equations
Directory of Open Access Journals (Sweden)
Laurent Delisle
2012-08-01
Full Text Available We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.
Wilets, Lawrence
1989-01-01
Successful modeling of quantum chromodynamics with a relativistic quark-soliton field theory has been developed over the past decade. As introduced by R Freidberg and T D Lee, the foundation of the model involves the chromodielectric properties of the physical vacuum, which yield absolute color confinement. The model allows for the consistent calculation of the dynamics of hadrons and hadronic reactions. The book summarizes and expands upon the extensive literature on the subject, concentrating on the Friedberg-Lee model and variations thereof. New results and future directions are included. T
Regularized degenerate multi-solitons
Correa, Francisco; Fring, Andreas
2016-09-01
We report complex {P}{T} -symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schrödinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota's direct method or on a nonlinear superposition obtained from multiple Bäcklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.
Soliton physics with semiconductor exciton-polaritons in confined systems
Sich, Maksym; Skryabin, Dmitry V.; Krizhanovskii, Dmitry N.
2016-10-01
In the past decade, there has been a significant progress in the study of non-linear polariton phenomena in semiconductor microcavities. One of the key features of non-linear systems is the emergence of solitons. The complexity and the inherently strong nonlinearity of the polariton system made it a perfect sandpit for observing solitonic effects in half-light half-matter environment. This review focuses on the theory and the latest experimental elucidating physics as well as potential applications of conservative and dissipative solitons in exciton-polariton systems. xml:lang="fr"
White-Light Nonlinear Photonic Lattices in Self-Defocusing Media
Institute of Scientific and Technical Information of China (English)
GAO Yuan-Mei; LIU Si-Min
2007-01-01
Using fully incoherent white light emitted from an incandescent lamp and amplitude mask, we experimentally investigate the influence of several factors on the fabrication of the lattice in photovoltaic self-defocusing LiNbO3:Fe crystal, the factors include the orientation of the crystalline c axis relative to the principal axis of the photonic lattice and the filament, the diameter of input dark spot and the separation of the adjacent input dark spots. Experimental results reveal that the best fabricating condition of photonic lattices is that the principal axis of lattice is tilted for 45° relative to the crystalline c axis which is parallel to the filament of the lamp. In addition, it is necessary that the diameter of the input dark spot is larger than the half of their separation.
A nonlinear lattice model for Heisenberg helimagnet and spin wave instabilities
Ludvin Felcy, A.; Latha, M. M.; Christal Vasanthi, C.
2016-10-01
We study the dynamics of a Heisenberg helimagnet by presenting a square lattice model and proposing the Hamiltonian associated with it. The corresponding equation of motion is constructed after averaging the Hamiltonian using a suitable wavefunction. The stability of the spin wave is discussed by means of Modulational Instability (MI) analysis. The influence of various types of inhomogeneities in the lattice is also investigated by improving the model.
Chirped Optical Solitons in Single-mode Birefringent Fibers.
Mahmood, M F
1996-12-01
The trapping behavior of two chirped solitons forming a bound state in a single-mode birefringent fiber is investigated on the basis of a model of coupled nonlinear Schroedinger equations. The positive initial chirp plays an important role in controlling the threshold amplitude for soliton trapping without causing excessive pulse broadening.
Strongly interacting matter at high densities with a soliton model
Johnson, Charles Webster
1998-12-01
differential equations for the quark wave functions and for the average meson field. It is convenient to work with the Dirac equation describing the quark sector in momentum space, while the nonlinear Klein-Gordon equation for the mean field is easier to solve in coordinate space. The boundary conditions required by the many- soliton problem can be easily accommodated in the Fourier series representation. Many of the technical difficulties arise from the need of transforming back-and-forth between coordinate space and momentum space in the course of the iteration of the coupled nonlinear differential equations. Solution of the coupled set of equations yields energy bands for sufficiently small lattice sizes. It is observed that the ground state energy first develops a minimum, followed by band intersections as the average density is increased. The intersection of the lowest bands can be identified with the transition to the high- energy phase (quark matter) in the model. The behavior of the in-medium properties of several physical quantities are also calculated as a function of the average density. (Abstract shortened by UMI.)
Coupled spatial multi-mode solitons in microcavity wires
Slavcheva, G; Pimenov, A
2016-01-01
A modal expansion approach is developed and employed to investigate and elucidate the nonlinear mechanism behind the multistability and formation of coupled multi-mode polariton solitons in microcavity wires. With pump switched on and realistic dissipation parameters, truncating the expansion up to the second-order wire mode, our model predicts two distinct coupled soliton branches: stable and ustable. Modulational stability of the homogeneous solution and soliton branches stability are studied. Our simplified 1D model is in remarkably good agreement with the full 2D mean-field Gross-Pitaevskii model, reproducing correctly the soliton existence domain upon variation of pump amplitude and the onset of multistability.
Radiation by solitons due to higher-order dispersion
DEFF Research Database (Denmark)
Karpman, V.I.
1993-01-01
We consider the Korteweg-de Vries (KdV) and nonlinear Schrodinger (NS) equations with higher-order derivative terms describing dispersive corrections. Conditions of existence of stationary and radiating solitons of the fifth-order KdV equation are obtained. An asymptotic time-dependent solution...... to the latter equation, describing the soliton radiation, is found. The radiation train may be in front as well as behind the soliton, depending on the sign of dispersion. The change rate of the soliton due to the radiation is calculated. A modification of the WKB method, that permits one to describe...
Modulation instability and solitons in two-color nematic crystals
Horikis, Theodoros P
2016-01-01
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis reveals that while the nonlocal term suppresses the growth rates, substantially, the coupled system exhibits significantly higher growth rates than its scalar counterpart. In the soliton case, the necessary conditions are derived that lead the solitons to exhibit stable, undistorted evolution, suppressing any breathing behavior and radiation, leading to soliton mutual guiding.