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.
On existence of soliton solutions of arbitrary-order system of nonlinear Schrodinger equations
International Nuclear Information System (INIS)
Zhestkov, S.V.
2003-01-01
The soliton solutions are constructed for the system of arbitrary-order coupled nonlinear Schrodinger equations . The necessary and sufficient conditions of existence of these solutions are obtained. It is shown that the maximum number of solitons in nondegenerate case is 4L, where L is order of the system. (author)
Damped nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
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...
International Nuclear Information System (INIS)
Zhestkov, S.V.; Romanenko, A.A.
2009-01-01
The problem of existence of soliton-like solutions of (1+1), (2+1), (3+1)-dimensional Schrodinger equations with the third power nonlinearity law is investigated. The numerical-analytical method of constructing solitons is developed. (authors)
International Nuclear Information System (INIS)
Tian Bo; Gao Yitian
2005-01-01
A realistic, inhomogeneous fiber in the optical communication systems can be described by the perturbed nonlinear Schrodinger model (also named as the normalized nonlinear Schrodinger model with periodically varying coefficients, dispersion managed nonlinear Schrodinger model or nonlinear Schrodinger model with variable coefficients). Hereby, we extend to this model a direct method, perform symbolic computation and obtain two families of the exact, analytic bright-solitonic solutions, with or without the chirp respectively. The parameters addressed include the shape of the bright soliton, soliton amplitude, inverse width of the soliton, chirp, frequency, center of the soliton and center of the phase of the soliton. Of optical and physical interests, we discuss some previously-published special cases of our solutions. Those solutions could help the future studies on the optical communication systems. ms
Soliton solutions for a quasilinear Schrodinger equation
Directory of Open Access Journals (Sweden)
Duchao Liu
2013-12-01
Full Text Available In this article, critical point theory is used to show the existence of nontrivial weak solutions to the quasilinear Schrodinger equation $$ -\\Delta_p u-\\frac{p}{2^{p-1}}u\\Delta_p(u^2=f(x,u $$ in a bounded smooth domain $\\Omega\\subset\\mathbb{R}^{N}$ with Dirichlet boundary conditions.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.......A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz...
Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet
2017-11-01
In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.
Semiclassical quantization of the nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nohl, C.R.
1976-01-01
Using the functional integral technique of Dashen, Hasslacher, and Neveu, we perform a semiclassical quantization of the nonlinear Schrodinger equation (NLSE), which reproduces McGuire's exact result for the energy levels of the bound states of the theory. We show that the stability angle formalism leads to the one-loop normal ordering and self-energy renormalization expected from perturbation theory, and demonstrate that taking into account center-of-mass motion gives the correct nonrelativistic energy--momentum relation. We interpret the classical solution in the context of the quantum theory, relating it to the matrix element of the field operator between adjacent bound states in the limit of large quantum numbers. Finally, we quantize the NLSE as a theory of N component fermion fields and show that the semiclassical method yields the exact energy levels and correct degeneracies
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...
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
... 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.
Collapse in a forced three-dimensional nonlinear Schrodinger equation
DEFF Research Database (Denmark)
Lushnikov, P.M.; Saffman, M.
2000-01-01
We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation.......We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation....
Travelling Solitons in the Damped Driven Nonlinear Schroedinger Equation
Barashenkov, I V
2003-01-01
The well-known effect of the linear damping on the moving nonlinear Schrodinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable.
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....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....
International Nuclear Information System (INIS)
Xiao Yafeng; Xue Haili; Zhang Hongqing
2011-01-01
Based on Jacobi elliptic function and the Lame equation, the perturbation method is applied to get the multi-order envelope periodic solutions of the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation. These multi-order envelope periodic solutions can degenerate into the different envelope solitary solutions. (authors)
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....
Nonlinear damped Schrodinger equation in two space dimensions
Directory of Open Access Journals (Sweden)
Tarek Saanouni
2015-04-01
Full Text Available In this article, we study the initial value problem for a semi-linear damped Schrodinger equation with exponential growth nonlinearity in two space dimensions. We show global well-posedness and exponential decay.
The matrix nonlinear Schrodinger equation in dimension 2
DEFF Research Database (Denmark)
Zuhan, L; Pedersen, Michael
2001-01-01
In this paper we study the existence of global solutions to the Cauchy problem for the matrix nonlinear Schrodinger equation (MNLS) in 2 space dimensions. A sharp condition for the global existence is obtained for this equation. This condition is in terms of an exact stationary solution...... of a semilinear elliptic equation. In the scalar case, the MNLS reduces to the well-known cubic nonlinear Schrodinger equation for which existence of solutions has been studied by many authors. (C) 2001 Academic Press....
On the solution of the nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Zayed, E.M.E.; Zedan, Hassan A.
2003-01-01
In this paper we study the nonlinear Schrodinger equation with respect to the unknown function S(x,t). New dimensional reduction and exact solution for a nonlinear Schrodinger equation are presented and a complete group classification is given with respect to the function S(x,t). Moreover, specializing the potential function S(x,t), new classes of invariant solution and group classification are obtained in the cases of physical interest
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
The study of solitons in those physical systems reveals some exciting .... With the following power series expansions for g(z,t) and f(z,t): g(z,t) = εg1(z,t) + ... If nonlinearity γ (z) is also taken as a function in figure 1b, the periodic and oscillation.
Nonlinear Schrodinger equation: A testing ground for the quantization of nonlinear waves
International Nuclear Information System (INIS)
Klein, A.; Krejs, F.
1976-01-01
Quantization of the nonlinear Schrodinger equation is carried out by the method due to Kerman and Klein. A viable procedure is inferred from the quantum interpretation of the classical (soliton) solution. The ground-state energy for a system with n particles is calculated to an accuracy which includes the first quantum correction to the semiclassical result. It is demonstrated that the exact answer can be obtained systematically only at the next level of approximation. For the calculation of the first quantum correction, the quantum theory of the stability of periodic orbits in field theory is developed and discussed. Since one is dealing with a finite many-body problem, the field theory can be written so that no infinite terms are encountered, but the Hamiltonian can also be artificially rearranged so as to destory this feature. For learning purposes the calculations are carried out with the various alternatives, and our methods prove capable of providing a uniform final result
Dynamics of breathers in discrete nonlinear Schrodinger models
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge
1998-01-01
We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...
Multiple solutions to some singular nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Monica Lazzo
2001-01-01
Full Text Available We consider the equation $$ - h^2 Delta u + V_varepsilon(x u = |u|^{p-2} u $$ which arises in the study of standing waves of a nonlinear Schrodinger equation. We allow the potential $V_varepsilon$ to be unbounded below and prove existence and multiplicity results for positive solutions.
Collapse arresting in an inhomogeneous quintic nonlinear Schrodinger model
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Schjødt-Eriksen, Jens; Christiansen, Peter Leth
1999-01-01
Collapse of (1 + 1)-dimensional beams in the inhomogeneous one-dimensional quintic nonlinear Schrodinger equation is analyzed both numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams in which the homogeneous medium would blow up...
Numerical study of fractional nonlinear Schrodinger equations
Klein, Christian
2014-10-08
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.
Averaging for solitons with nonlinearity management
International Nuclear Information System (INIS)
Pelinovsky, D.E.; Kevrekidis, P.G.; Frantzeskakis, D.J.
2003-01-01
We develop an averaging method for solitons of the nonlinear Schroedinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations
Universality in an information-theoretic motivated nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Parwani, R; Tabia, G
2007-01-01
Using perturbative methods, we analyse a nonlinear generalization of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of the nonlinearity scale, to the energy eigenvalues of the linear Schrodinger equation in the presence of an external potential and observe some generic features. In one space dimension these are (i) for nodeless ground states, the energy shifts are subleading in the nonlinearity parameter compared to the shifts for the excited states; (ii) the shifts for the excited states are due predominantly to contribution from the nodes of the unperturbed wavefunctions, and (iii) the energy shifts for excited states are positive for small values of a regulating parameter and negative at large values, vanishing at a universal critical value that is not manifest in the equation. Some of these features hold true for higher dimensional problems. We also study two exactly solved nonlinear Schrodinger equations so as to contrast our observations. Finally, we comment on the possible significance of our results if the nonlinearity is physically realized
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
Spinning solitons in cubic-quintic nonlinear media ... features of families of bright vortex solitons (doughnuts, or 'spinning' solitons) in both conservative and dissipative cubic-quintic nonlinear media. ... Pramana – Journal of Physics | News.
Solutions to nonlinear Schrodinger equations for special initial data
Directory of Open Access Journals (Sweden)
Takeshi Wada
2015-11-01
Full Text Available This article concerns the solvability of the nonlinear Schrodinger equation with gauge invariant power nonlinear term in one space dimension. The well-posedness of this equation is known only for $H^s$ with $s\\ge 0$. Under some assumptions on the nonlinearity, this paper shows that this equation is uniquely solvable for special but typical initial data, namely the linear combinations of $\\delta(x$ and p.v. (1/x, which belong to $H^{-1/2-0}$. The proof in this article allows $L^2$-perturbations on the initial data.
Reduction of the state vector by a nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Pearle, P.
1976-01-01
It is hypothesized that the state vector describes the physical state of a single system in nature. Then it is necessary that the state vector of a macroscopic apparatus not assume the form of a superposition of macroscopically distinguishable state vectors. To prevent this, it is suggested that a nonlinear term be added to the Schrodinger equation, which rapidly drives the amplitude of one or another of the state vectors in such a superposition to one, and the rest to zero. It is proposed that it is the phase angles of the amplitudes immediately after a measurement which determine which amplitude is driven to one. A diffusion equation is arrived at to describe the reduction of an ensemble of state vectors corresponding to an ensemble of macroscopically identically prepared experiments. Then a nonlinear term to add to the Schrodinger equation is presented, and it is shown that this leads to the diffusion equation in a weak-coupling approximation
Exact solutions of a nonpolynomially nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Parwani, R.; Tan, H.S.
2007-01-01
A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics
Walking solitons in quadratic nonlinear media
Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru
1996-01-01
We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed
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...... in the third derivative term) and vanish at alpha3 -->0. The most essential, at small alpha (3), is a quasisoliton emitting resonant radiation (resonantly radiating soliton). Its relationship with the other (steady) quasisoliton, called embedded soliton, is studied analytically and also in numerical...
Self-similar solutions of the modified nonlinear schrodinger equation
International Nuclear Information System (INIS)
Kitaev, A.V.
1986-01-01
This paper considers a 2 x 2 matrix linear ordinary differential equation with large parameter t and irregular singular point of fourth order at infinity. The leading order of the monodromy data of this equation is calculated in terms of its coefficients. Isomonodromic deformations of the equation are self-similar solutions of the modified nonlinear Schrodinger equation, and therefore inversion of the expressions obtained for the monodromy data gives the leading term in the time-asymptotic behavior of the self-similar solution. The application of these results to the type IV Painleve equation is considered in detail
Ring vortex solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Briedis, D.; Petersen, D.E.; Edmundson, D.
2005-01-01
We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single...... 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....
Asymptotic behavior for a quadratic nonlinear Schrodinger equation
Directory of Open Access Journals (Sweden)
Pavel I. Naumkin
2008-02-01
Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.
Stokes phenomena and monodromy deformation problem for nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Chowdury, A.R.; Naskar, M.
1986-01-01
Following Flaschka and Newell, the inverse problem for Painleve IV is formulated with the help of similarity variables. The Painleve IV arises as the eliminant of the two second-order ordinary differential equations originating from the nonlinear Schrodinger equation. Asymptotic expansions are obtained near the singularities at zero and infinity of the complex eigenvalue plane. The corresponding analysis then displays the Stokes phenomena. The monodromy matrices connecting the solution Y /sub j/ in the sector S /sub j/ to that in S /sub j+1/ are fixed in structure by the imposition of certain conditions. It is then shown that a deformation keeping the monodromy data fixed leads to the nonlinear Schrodinger equation. While Flaschka and Newell did not make any absolute determination of the Stokes parameters, the present approach yields the values of the Stokes parameters in an explicit way, which in turn can determine the matrix connecting the solutions near zero and infinity. Finally, it is shown that the integral equation originating from the analyticity and asymptotic nature of the problem leads to the similarity solution previously determined by Boiti and Pampinelli
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm
2010-01-01
We show that the two-dimensional, nonlinear Schrodinger 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 e...
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...
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...
On the so called rogue waves in nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Y. Charles Li
2016-04-01
Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.
International Nuclear Information System (INIS)
Bullough, R.K.
1978-01-01
Two sorts of solitons are considered - the classical soliton, a solitary wave which shows great stability in collision with other solitary waves, and the quantal, that is quantised, soliton. Solitons as mathematical objects have excited theoreticians because of their wide ranging applications in physics. They appear as solutions of particular nonlinear wave equations which often have a certain universal significance. The importance of solitons in modern physics is discussed with especial reference to; nonlinearity and solitons, the nonlinear Schroedinger equation, the sine-Gordon equation, notional spins and particle physics. (U.K.)
Spatiotemporal solitons in quadratic nonlinear media
Indian Academy of Sciences (India)
Optical solitons are localized electromagnetic waves that propagate stably in .... conversion generates a nonlinear phase shift ∆ΦNL at the FH frequency. ... to incidence on the SHG crystal (lithium iodate or barium borate, cut for type-I interac-.
Solitons and nonlinear waves in space plasmas
International Nuclear Information System (INIS)
Stasiewicz, K.
2005-01-01
Recent measurements made on the ESA/NASA Cluster mission to the Earth's magnetosphere have provided first detailed measurements of magnetosonic solitons in space. The solitons represent localized enhancements of the magnetic field by a factor of 2-10, or depressions down to 10% of the ambient field. The magnetic field signatures are associated with density depressions/enhancements A two-fluid model of nonlinear electron and ion inertial waves in anisotropic plasmas explains the main properties of these structures. It is shown that warm plasmas support four types of nonlinear waves, which correspond to four linear modes: Alfvenic, magnetosonic, sound, and electron inertial waves. Each of these nonlinear modes has slow and fast versions. It is shown by direct integration that the exponential growth rate of nonlinear modes is balanced by the ion and electron dispersion leading to solutions in the form of trains of solitons or cnoidal waves. By using a novel technique of phase portraits it is shown how the dispersive properties of electron and ion inertial waves change at the transition between warm and hot plasmas, and how trains of solitons ('' mirror modes '') are produced in a hot, anisotropic plasma. The applicability of the model is illustrated with data from Cluster spacecraft. (author)
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....
Rational solitons in deep nonlinear optical Bragg grating
Alatas, H.; Iskandar, A.A.; Tjia, M.O.; Valkering, T.P.
2006-01-01
We have examined the rational solitons in the Generalized Coupled Mode model for a deep nonlinear Bragg grating. These solitons are the degenerate forms of the ordinary solitons and appear at the transition lines in the parameter plane. A simple formulation is presented for the investigation of the
Creation and annihilation of solitons in the string nonlinear equation
International Nuclear Information System (INIS)
Aguero G, M.A.; Espinosa G, A.A.; Martinez O, J.
1997-01-01
Starting from the cubic-quintic Schroedinger equation it is obtained the nonlinear string equation. This system supports regular and singular solitons. It is shown that two singular solitons could be generated after the interaction of two regular solitons and viceversa. (Author)
Travelling solitons in the parametrically driven nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Barashenkov, I.V.; Zemlyanaya, E.V.; Baer, M.
2000-01-01
We show that the parametrically driven nonlinear Schroedinger equation has wide classes of travelling soliton solutions, some of which are stable. For small driving strengths stable nonpropagating and moving solitons co-exist while strongly forced solitons can only be stable when moving sufficiently fast
Directory of Open Access Journals (Sweden)
M.G. Hafez
2016-06-01
Full Text Available In this paper, the novel (G′/G-expansion method is applied to construct exact travelling wave solutions of the cubic nonlinear Schrodinger equation. This technique is straightforward and simple to use, and gives more new general solutions than the other existing methods. Various types of solitary and periodic wave solutions of this equation are derived. The obtained results may be helpful to describe the wave propagation in soliton physics, such as soliton propagation in optical fibers, modulus instability in plasma physics, etc. and provided us the firm mathematical foundation in soliton physics or any varied instances. Furthermore, three-dimensional modules plot of the solutions are also given to visualize the dynamics of the equation.
Nonlinear compression of optical solitons
Indian Academy of Sciences (India)
linear pulse propagation is the nonlinear Schrödinger (NLS) equation [1]. There are ... Optical pulse compression finds important applications in optical fibres. The pulse com ..... to thank CSIR, New Delhi for financial support in the form of SRF.
Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media
International Nuclear Information System (INIS)
Zhong Weiping; Yi Lin; Yang Zhengping; Xie Ruihua; Milivoj, Belic; Chen Goong
2008-01-01
Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through
Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems
Directory of Open Access Journals (Sweden)
Hailiang Li
2003-09-01
Full Text Available This paper concerns the well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks appear in the limit system. We establish the existence of a global solution and show the time-asymptotic behavior of a classical solutions of Schrodinger-Poisson system for a fixed re-scaled Planck constant.
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.
Topological soliton solutions for some nonlinear evolution equations
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Ahmet Bekir
2014-03-01
Full Text Available In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc. envelope for the understanding of most nonlinear physical phenomena.
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.
Staggered and short-period solutions of the saturable discrete nonlinear Schrodinger equation
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, K.O.; Samuelsen, Mogens Rugholm
2009-01-01
We point out that the nonlinear Schrodinger lattice with a saturable nonlinearity also admits staggered periodic aswell 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 ...
Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping
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Eleni Bisognin
2007-01-01
Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.
Polynomially decaying transmission for the nonlinear schrodinger equation in a random medium
International Nuclear Information System (INIS)
Devillard, P.; Sovillard, B.
1986-01-01
This is the first study of one the transmission problems associate to the nonlinear Schrodinger equation with a random potential. We show that for almost every realization of the medium the rate of transmission vanishes when increasing the size of the medium; however, whereas it decays exponentially in the linear regime, it decays polynomially in the nonlinear one
Existence and concentration of semiclassical states for nonlinear Schrodinger equations
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Shaowei Chen
2012-05-01
Full Text Available In this article, we study the semilinear Schrodinger equation $$ -epsilon^2Delta u+ u+ V(xu=f(u,quad uin H^1(mathbb{R}^N, $$ where $Ngeq 2$ and $epsilon>0$ is a small parameter. The function $V$ is bounded in $mathbb{R}^N$, $inf_{mathbb{R}^N}(1+V(x>0$ and it has a possibly degenerate isolated critical point. Under some conditions on f, we prove that as $epsilono 0$, this equation has a solution which concentrates at the critical point of V.
International Nuclear Information System (INIS)
Bouard, Anne de; Debussche, Arnaud
2006-01-01
In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1
International Nuclear Information System (INIS)
Esrick, M.A.
1981-01-01
A time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter is derived from the Gor'kov equations. Three types of traveling wave solutions of the equation are discussed. The phases and amplitudes of these solutions propagate at different speeds. The first type of solution has an amplitude that propagates as a soliton and it is suggested that this solution might correspond to the recently observed propagating collective modes of the order parameter. The amplitude of the second type of solution propagates as a periodic disturbance in space and time. It is suggested that this type of solution might explain the recently observed multiple values of the superconductor energy gap as well as the spatially inhomogenous superconducting state. The third type of solution, which is of a more general character, might provide some insight into non-periodic, inhomogeneous states occuring in superconductors. It is also proposed that quasiparticle injection and microwave irradiation might generate soliton-like disturbances in superconductors
Stationary walking solitons in bulk quadratic nonlinear media
Mihalache, Dumitru; Mazilu, D; Crasonavn, L C; Torner Sabata, Lluís
1997-01-01
We study the mutual trapping of fundamental and second-harmonic light beams propagating in bulk quadratic nonlinear media in the presence of Poynting vector beam walk-off. We show numerically the existence of a two-parameter family of (2 + 1)-dimensional stationary, spatial walking solitons. We have found that the solitons exist at various values of material parameters with different wave intensities and soliton velocities. We discuss the differences between (2 + 1) and (1 + 1)-dimensional wa...
Spiraling solitons and multipole localized modes in nonlocal nonlinear media
International Nuclear Information System (INIS)
Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.; Bang, Ole; Krolikowski, Wieslaw; Kivshar, Yuri S.
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 different 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
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....
Curvature-induced symmetry breaking in nonlinear Schrodinger models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Mingaleev, S. F.; Christiansen, Peter Leth
2000-01-01
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states...
Exact solutions of nonlinear generalizations of the Klein Gordon and Schrodinger equations
International Nuclear Information System (INIS)
Burt, P.B.
1978-01-01
Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given. 14 references
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...
DEFF Research Database (Denmark)
Rasmussen, Kim; Christiansen, Peter Leth; Johansson, Magnus
1998-01-01
A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exp...
Global well-posedness for nonlinear Schrodinger equations with energy-critical damping
Directory of Open Access Journals (Sweden)
Binhua Feng
2015-01-01
Full Text Available We consider the Cauchy problem for the nonlinear Schrodinger equations with energy-critical damping. We prove the existence of global in-time solutions for general initial data in the energy space. Our results extend some results from [1,2].
On a quantum version of conservation laws for derivative nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Sen, S.; Chowdhury, A.R.
1988-01-01
The authors derived the quantum mechanical versions of infinite number of conservation laws associated with Derivative Nonlinear Schrodinger equation with the help of a methodology used in string theory. The renormalised version of the conserved quantities are obtained with explicit forms of the counter terms
Collapse arresting in an inhomogeneous two-dimensional nonlinear Schrodinger model
DEFF Research Database (Denmark)
Schjødt-Eriksen, Jens; Gaididei, Yuri Borisovich; Christiansen, Peter Leth
2001-01-01
Collapse of (2 + 1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrodinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may...
A study on linear and nonlinear Schrodinger equations by the variational iteration method
International Nuclear Information System (INIS)
Wazwaz, Abdul-Majid
2008-01-01
In this work, we introduce a framework to obtain exact solutions to linear and nonlinear Schrodinger equations. The He's variational iteration method (VIM) is used for analytic treatment of these equations. Numerical examples are tested to show the pertinent features of this method
Nonlinear Klein-Gordon soliton mechanics
International Nuclear Information System (INIS)
Reinisch, G.
1992-01-01
Nonlinear Klein-Gordon solitary waves - or solitons in a loose sense - in n+1 dimensions, driven by very general external fields which must only satisfy continuity - together with regularity conditions at the boundaries of the system, obey a quite simple equation of motion. This equation is the exact generalization to this dynamical system of infinite number of degrees of freedom - which may be conservative or not - of the second Newton's law setting the basis of material point mechanics. In the restricted case of conservative nonlinear Klein-Gordon systems, where the external driving force is derivable from a potential energy, we recover the generalized Ehrenfest theorem which was itself the extension to such systems of the well-known Ehrenfest theorem in quantum mechanics. This review paper first displays a few (of one-dimensional sine-Gordon type) typical examples of the basic difficulties related to the trial construction of solitary-waves is proved and the derivation of the previous sine-Gordon examples from this theorem is displayed. Two-dimensional nonlinear solitary-wave patterns are considered, as well as a special emphasis is put on the applications to space-time complexity of 1-dim. sine-Gordon systems
Directory of Open Access Journals (Sweden)
Magdy A. El-Tawil
2009-01-01
Full Text Available A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.
Soliton interaction in the coupled mixed derivative nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Zhang Haiqiang; Tian Bo; Lue Xing; Li He; Meng Xianghua
2009-01-01
The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schroedinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.
Modified wave operators for nonlinear Schrodinger equations in one and two dimensions
Directory of Open Access Journals (Sweden)
Nakao Hayashi
2004-04-01
Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13
DEFF Research Database (Denmark)
leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2004-01-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...... losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials....
A discrete homotopy perturbation method for non-linear Schrodinger equation
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H. A. Wahab
2015-12-01
Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.
Solitary waves for a coupled nonlinear Schrodinger system with dispersion management
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Panayotis Panayotaros
2010-08-01
Full Text Available We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions's Concentration Compactness principle to show the existence of standing waves with prescribed L^2 norm in an averaged equation that approximates the coupled system. We also use the Mountain Pass Lemma to prove the existence of standing waves with prescribed frequencies.
Hs solutions for nonlinear Schrodinger equations with potentials superquadratic at infinity
International Nuclear Information System (INIS)
Zhang Guoping; Yajima, Kenji; Liu Fengshan
2006-01-01
In this Letter we study the initial value problem for the nonlinear Schrodinger equation with the potential V superquadratic at infinity. With the local smoothing property and Strichartz inequality obtained by the authors, we prove the existence and the uniqueness of the solution for H s -valued initial data and fractional s by combining the L 2 boundedness theory of pseudo differential operators and the fractional derivatives estimate
Travelling solitons in the damped driven nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Barashenkov, I.V.; Zemlyanaya, E.V.
2003-01-01
The well known effect of the linear damping on the moving nonlinear Schroedinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable
Solitons in PT-symmetric potential with competing nonlinearity
International Nuclear Information System (INIS)
Khare, Avinash; Al-Marzoug, S.M.; Bahlouli, Hocine
2012-01-01
We investigate the effect of competing nonlinearities on beam dynamics in PT-symmetric potentials. In particular, we consider the stationary nonlinear Schrödinger equation (NLSE) in one dimension with competing cubic and generalized nonlinearity in the presence of a PT-symmetric potential. Closed form solutions for localized states are obtained. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow associated with these complex solitons is also examined. -- Highlights: ► Effect of competing nonlinearities on beam dynamics in PT-symmetric potentials. ► Closed form solutions for localized states are. ► The transverse power flow associated with these complex solitons is also examined.
Soliton excitations in a class of nonlinear field theory models
International Nuclear Information System (INIS)
Makhan'kov, V.G.; Fedyanin, V.K.
1985-01-01
Investigation results of nonlinear models of the field theory with a lagrangian are described. The theory includes models both with zero stable vacuum epsilon=1 and with condensate epsilon=-1 (of disturbed symmetry). Conditions of existence of particle-like solutions (PLS), stability of these solutions are investigated. Soliton dynamics is studied. PLS formfactors are calculated. Statistical mechanics of solitons is built and their dynamic structure factors are calculated
Solitons supported by localized nonlinearities in periodic media
International Nuclear Information System (INIS)
Dror, Nir; Malomed, Boris A.
2011-01-01
Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BEC's) loaded into optical lattices, are often described by the nonlinear Schroedinger or Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single δ function or a combination of two δ functions. With the attractive or repulsive sign of the nonlinearity, this model gives rise to ordinary solitons or gap solitons (GS's), which reside, respectively, in the semi-infinite or finite gaps of the system's linear spectrum, being pinned to the δ functions. Physical realizations of these systems are possible in optics and BEC's, using diverse variants of the nonlinearity management. First, we demonstrate that the single δ function multiplying the nonlinear term supports families of stableregular solitons in the self-attractive case, while a family of solitons supported by the attractive δ function in the absence of the periodic potential is completely unstable. In addition, we show that the δ function can support stable GS's in the first finite band gap in both the self-attractive and repulsive models. The stability analysis for the GS's in the second finite band gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single δ function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two δ functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the δ functions set symmetrically with respect to the minimum or maximum of the underlying potential.
Tchen, C. M.
1986-01-01
Theoretical and numerical works in atmospheric turbulence have used the Navier-Stokes fluid equations exclusively for describing large-scale motions. Controversy over the existence of an average temperature gradient for the very large eddies in the atmosphere suggested that a new theoretical basis for describing large-scale turbulence was necessary. A new soliton formalism as a fluid analogue that generalizes the Schrodinger equation and the Zakharov equations has been developed. This formalism, processing all the nonlinearities including those from modulation provided by the density fluctuations and from convection due to the emission of finite sound waves by velocity fluctuations, treats large-scale turbulence as coalescing and colliding solitons. The new soliton system describes large-scale instabilities more explicitly than the Navier-Stokes system because it has a nonlinearity of the gradient type, while the Navier-Stokes has a nonlinearity of the non-gradient type. The forced Schrodinger equation for strong fluctuations describes the micro-hydrodynamical state of soliton turbulence and is valid for large-scale turbulence in fluids and plasmas where internal waves can interact with velocity fluctuations.
Xie, Xi-Yang; Tian, Bo; Liu, Lei; Guan, Yue-Yang; Jiang, Yan
2017-06-01
In this paper, we investigate a generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. Under certain integrable constraints, bilinear forms, bright one- and two-soliton solutions are obtained. Via certain transformation, we investigate the properties of the solitons with the first-order dispersion parameter σ1(x, t), second-order dispersion parameter σ2(x, t), third-order dispersion parameter σ3(x, t), phase modulation and gain (loss) v(x, t). Soliton propagation and collision are graphically presented and analyzed: One soliton is shown to maintain its amplitude and width during the propagation. When we choose σ1(x, t), σ2(x, t) and σ3(x, t) differently, travelling direction of the soliton is found to alter. v(x, t) is observed to affect the amplitude of the soliton. Head-on collision between the two solitons is presented with σ1(x, t), σ2(x, t), σ3(x, t) and v(x, t) as the constants, and solitons' amplitudes are the same before and after the collision. When σ1(x, t), σ2(x, t) and σ3(x, t) are chosen as certain functions, the solitons' traveling directions change during the collision. v(x, t) can influence the amplitudes of the two solitons.
Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.
2007-01-01
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves
Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential
Directory of Open Access Journals (Sweden)
Runzhang Xu
2012-11-01
Full Text Available This article studies a nonlinear Schodinger equation with harmonic potential by constructing different cross-constrained problems. By comparing the different cross-constrained problems, we derive different sharp criterion and different invariant manifolds that separate the global solutions and blowup solutions. Moreover, we conclude that some manifolds are empty due to the essence of the cross-constrained problems. Besides, we compare the three cross-constrained problems and the three depths of the potential wells. In this way, we explain the gaps in [J. Shu and J. Zhang, Nonlinear Shrodinger equation with harmonic potential, Journal of Mathematical Physics, 47, 063503 (2006], which was pointed out in [R. Xu and Y. Liu, Remarks on nonlinear Schrodinger equation with harmonic potential, Journal of Mathematical Physics, 49, 043512 (2008].
Quadratic soliton self-reflection at a quadratically nonlinear interface
Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai
2003-11-01
The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.
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...
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Abstract. In this paper, we obtain exact soliton solutions of the modified KdV equation, inho- mogeneous nonlinear Schrödinger equation and G(m, n) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the ...
Embedded solitons in the third-order nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Pal, Debabrata; Ali, Sk Golam; Talukdar, B
2008-01-01
We work with a sech trial function with space-dependent soliton parameters and envisage a variational study for the nonlinear Schoedinger (NLS) equation in the presence of third-order dispersion. We demonstrate that the variational equations for pulse evolution in this NLS equation provide a natural basis to derive a potential model which can account for the existence of a continuous family of embedded solitons supported by the third-order NLS equation. Each member of the family is parameterized by the propagation velocity and co-efficient of the third-order dispersion
Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation
Energy Technology Data Exchange (ETDEWEB)
Mani Rajan, M.S., E-mail: senthilmanirajanofc@gmail.com [Department of Physics, Anna University, Madurai Region, Ramanathapuram (India); Mahalingam, A. [Department of Physics, Anna University, Chennai - 600 025 (India); Uthayakumar, A. [Department of Physics, Presidency College, Chennai - 600 005 (India)
2014-07-15
We investigated the soliton solution for N coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons, study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management. -- Highlights: •We consider the nonlinear tunneling of soliton in birefringence fiber. •3-coupled NLS (CNLS) equation with variable coefficients is considered. •Two soliton solutions are obtained via Darboux transformation using constructed Lax pair. •Soliton tunneling through dispersion barrier and well are investigated. •Finally, cascade compression of soliton has been achieved.
Electron–soliton dynamics in chains with cubic nonlinearity
International Nuclear Information System (INIS)
Sales, M O; Moura, F A B F de
2014-01-01
In our work, we consider the problem of electronic transport mediated by coupling with solitonic elastic waves. We study the electronic transport in a 1D unharmonic lattice with a cubic interaction between nearest neighboring sites. The electron-lattice interaction was considered as a linear function of the distance between neighboring atoms in our study. We numerically solve the dynamics equations for the electron and lattice and compute the dynamics of an initially localized electronic wave-packet. Our results suggest that the solitonic waves that exist within this nonlinear lattice can control the electron dynamics along the chain. Moreover, we demonstrate that the existence of a mobile electron–soliton pair exhibits a counter-intuitive dependence with the value of the electron-lattice coupling. (paper)
Collective states of externally driven, damped nonlinear Schroedinger solitons
International Nuclear Information System (INIS)
Barashenkov, I.V.; Smirnov, Yu.S.
1997-01-01
We study bifurcations of localized stationary solitons of the externally driven, damped nonlinear Schroedinger equation iΨ t + Ψ xx + 2|Ψ| 2 Ψ=-iγΨ-h e iΩt , in the region of large γ (γ>1/2). For each pair of h and γ, there are two coexisting solitons, Ψ + and Ψ - . As the driver's strength h increases for the fixed γ, the Ψ + soliton merges with the flat background while the Ψ - forms a stationary collective state with two 'psi-pluses': Ψ - → Ψ (+ - +) . We obtain other stationary solutions and identify them as multisoliton complexes Ψ (++) , Ψ (--) , Ψ (-+) , Ψ (---) , Ψ (-+- ) etc. The corresponding intersoliton separations are compared to predictions of a variational approximation
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.
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
Defect solitons in saturable nonlinearity media with parity-time symmetric optical lattices
Energy Technology Data Exchange (ETDEWEB)
Hu, Sumei [Department of Physics, Guangdong University of Petrochemical Technology, Maoming 525000 (China); Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631 (China); Hu, Wei, E-mail: huwei@scnu.edu.cn [Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631 (China)
2013-11-15
We reported the existence and stability of defect solitons in saturable nonlinearity media with parity-time (PT) symmetric optical lattices. Families of fundamental and dipole solitons are found in the semi-infinite gap and the first gap. The power of solitons increases with the increasing of the propagation constant and saturation parameter. The existence areas of fundamental and dipole solitons shrink with the growth of saturation parameter. The instability of dipole solitons for positive and no defect induced by the imaginary part of PT symmetric potentials can be suppressed by the saturation nonlinearity, but for negative defect it cannot be suppressed by the saturation nonlinearity.
Spatiotemporal electromagnetic soliton and spatial ring formation in nonlinear metamaterials
International Nuclear Information System (INIS)
Zhang Jinggui; Wen Shuangchun; Xiang Yuanjiang; Wang Youwen; Luo Hailu
2010-01-01
We present a systematic investigation of ultrashort electromagnetic pulse propagation in metamaterials (MMs) with simultaneous cubic electric and magnetic nonlinearity. We predict that spatiotemporal electromagnetic solitons may exist in the positive-index region of a MM with focusing nonlinearity and anomalous group velocity dispersion (GVD), as well as in the negative-index region of the MM with defocusing nonlinearity and normal GVD. The experimental circumstances for generating and manipulating spatiotemporal electromagnetic solitons can be created by elaborating appropriate MMs. In addition, we find that, in the negative-index region of a MM, a spatial ring may be formed as the electromagnetic pulse propagates for focusing nonlinearity and anomalous GVD; while the phenomenon of temporal splitting of the electromagnetic pulse may appear for the same case except for the defocusing nonlinearity. Finally, we demonstrate that the nonlinear magnetization makes the sign of effective electric nonlinear effect switchable due to the combined action of electric and magnetic nonlinearity, exerting a significant influence on the propagation of electromagnetic pulses.
Nonlinear mode conversion with chaotic soliton generation at plasma resonance
International Nuclear Information System (INIS)
Pietsch, H.; Laedke, E.W.; Spatschek, K.H.
1993-01-01
The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations
Soliton dynamics in periodic system with different nonlinear media
International Nuclear Information System (INIS)
Zabolotskij, A.A.
2001-01-01
To analyze pulse dynamics in the optical system consisting of periodic sequence of nonlinear media one uses a composition model covering a model of resonance interaction of light ultrashort pulse with energy transition of medium with regard to pumping of the upper level and quasi-integrable model describing propagation of light field in another medium with cubic nonlinearity and dispersion. One additionally takes account of losses and other types of interaction in the from of perturbation members. On the basis of the method of scattering back problem and perturbation theory one developed a simple method to study peculiarities of soliton evolution in such periodic system. Due to its application one managed to describe different modes of soliton evolution in such a system including chaotic dynamics [ru
Soliton solutions of coupled nonlinear Klein-Gordon equations
International Nuclear Information System (INIS)
Alagesan, T.; Chung, Y.; Nakkeeran, K.
2004-01-01
The coupled nonlinear Klein-Gordon equations are analyzed for their integrability properties in a systematic manner through Painleve test. From the Painleve test, by truncating the Laurent series at the constant level term, the Hirota bilinear form is identified, from which one-soliton solutions are derived. Then, the results are generalized to the two, three and N-coupled Klein-Gordon equations
International Nuclear Information System (INIS)
Li Biao; Chen Yong
2007-01-01
In this paper, the inhomogeneous nonlinear Schroedinger equation with the loss/gain and the frequency chirping is investigated. With the help of symbolic computation, three families of exact analytical solutions are presented by employing the extended projective Riccati equation method. From our results, many previous known results of nonlinear Schroedinger equation obtained by some authors can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. Of optical and physical interests, soliton propagation and soliton interaction are discussed and simulated by computer, which include snake-soliton propagation and snake-solitons interaction, boomerang-like soliton propagation and boomerang-like solitons interaction, dispersion managed (DM) bright (dark) soliton propagation and DM solitons interaction
Rational solitons in the parity-time-symmetric nonlocal nonlinear Schrödinger model
International Nuclear Information System (INIS)
Li Min; Xu Tao; Meng Dexin
2016-01-01
In this paper, via the generalized Darboux transformation, rational soliton solutions are derived for the parity-time-symmetric nonlocal nonlinear Schrödinger (NLS) model with the defocusing-type nonlinearity. We find that the first-order solution can exhibit the elastic interactions of rational antidark-antidark, dark-antidark, and antidark-dark soliton pairs on a continuous wave background, but there is no phase shift for the interacting solitons. Also, we discuss the degenerate case in which only one rational dark or antidark soliton survives. Moreover, we reveal that the second-order rational solution displays the interactions between two solitons with combined-peak-valley structures in the near-field regions, but each interacting soliton vanishes or evolves into a rational dark or antidark soliton as |z| → ∞. In addition, we numerically examine the stability of the first- and second-order rational soliton solutions. (author)
Energy Technology Data Exchange (ETDEWEB)
Matsumura, M. [Shizuoka University, Shizuoka (Japan); Nagatani, T. [Shizuoka University, Shizuoka (Japan). Faculty of Engineering
1999-07-25
Traffic jams are investigated numerically and analystically in the optimal velocity model on a single-line highway. The condition is found whether or not traffic jams occur when a car stops instantly. It is shown that traffic soliton appears 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 point. The soliton obtained from the nonlinear analysis is consistent with that of the numerical simulation. (author)
SOLUCIÓN DE LA ECUACIÓN NO LINEAL DE SCHRODINGER (1+1 EN UN MEDIO KERR
Directory of Open Access Journals (Sweden)
Francis Armando Segovia
2015-12-01
Full Text Available Se presenta un marco teórico y se muestra una simulación numérica de la propagación de solitones. Con especial atención a los solitones ópticos espaciales, se calcula analíticamente el perfil de solitón correspondiente a la ecuación Schrodinger no-lineal para un medio Kerr. Los resultados muestran que los solitones ópticos son pulsos estables cuya forma y espectro son preservados en grandes distancias.Solution of the nonlinear Schrodinger equation (1+1 in a Kerr mediumABSTRACTThis document presents a theoretical framework and shows a numerical simulation for the propagation of solitons. With special attention to the spatial optical solitons, we calculates analytically the profile of solitón corresponding to the non-linear Schrodinger equation for a Kerr medium. The results show that the optical solitons are stable pulses whose shape and spectrum are preserved at great distances.Keywords: nonlinear optics, nonlinear Schrodinger equation, solitons.
Directory of Open Access Journals (Sweden)
Jinmyoung Seok
2015-07-01
Full Text Available In this article, we are interested in singularly perturbed nonlinear elliptic problems involving a fractional Laplacian. Under a class of nonlinearity which is believed to be almost optimal, we construct a positive solution which exhibits multiple spikes near any given local minimum components of an exterior potential of the problem.
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav; Růžička, František; Zloshchastiev, K. G.
2017-01-01
Roč. 9, č. 8 (2017), č. článku 165. ISSN 2073-8994 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : PT symmetry * nonlinear Schrodinger equations * logarithmic nonlinearities Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.457, year: 2016
Gap solitons under competing local and nonlocal nonlinearities
International Nuclear Information System (INIS)
Kuo, Kuan-Hsien; Lin Yuanyao; Lee, Ray-Kuang; Malomed, Boris A.
2011-01-01
We analyze the existence, bifurcations, and shape transformations of one-dimensional gap solitons (GSs) in the first finite band gap induced by a periodic potential built into materials with local self-focusing and nonlocal self-defocusing nonlinearities. Originally stable on-site GS modes become unstable near the upper edge of the band gap with the introduction of the nonlocal self-defocusing nonlinearity with a small nonlocality radius. Unstable off-site GSs bifurcate into a new branch featuring single-humped, double-humped, and flat-top modes due to the competition between local and nonlocal nonlinearities. The mechanism underlying the complex bifurcation pattern and cutoff effects (termination of some bifurcation branches) is illustrated in terms of the shape transformation under the action of the varying degree of the nonlocality. The results of this work suggest a possibility of optical-signal processing by means of the competing nonlocal and local nonlinearities.
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.
DEFF Research Database (Denmark)
Bache, Morten; Moses, J.; Wise, F.W.
2010-01-01
Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)].......Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)]....
Self-similar solutions with compactly supported profile of some nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Pascal Begout
2014-04-01
Full Text Available ``Sharp localized'' solutions (i.e. with compact support for each given time t of a singular nonlinear type Schr\\"odinger equation in the whole space $\\mathbb{R}^N$ are constructed here under the assumption that they have a self-similar structure. It requires the assumption that the external forcing term satisfies that $\\mathbf{f}(t,x=t^{-(\\mathbf{p}-2/2}\\mathbf{F}(t^{-1/2}x$ for some complex exponent $\\mathbf{p}$ and for some profile function $\\mathbf{F}$ which is assumed to be with compact support in $\\mathbb{R}^N$. We show the existence of solutions of the form $\\mathbf{u}(t,x=t^{\\mathbf{p}/2}\\mathbf{U}(t^{-1/2}x$, with a profile $\\mathbf{U}$, which also has compact support in $\\mathbb{R}^N$. The proof of the localization of the support of the profile $\\mathbf{U}$ uses some suitable energy method applied to the stationary problem satisfied by $\\mathbf{U}$ after some unknown transformation.
Nonlinear de Broglie waves and the relation between relativistic and nonrelativistic solitons
International Nuclear Information System (INIS)
Barut, A.O.; Baby, B.V.
1988-07-01
It is shown that the well-known envelope soliton and kink solutions of the nonlinear Schroedinger equation are the nonrelativistic limit of the corresponding solutions of the nonlinear Klein-Gordon equation. 34 refs
Stability of Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity
International Nuclear Information System (INIS)
Dasanayaka, Sahan; Atai, Javid
2010-01-01
We investigate the existence and stability of Bragg grating solitons in a cubic-quintic medium with dispersive reflectivity. It is found that the model supports two disjoint families of solitons. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity. On the other hand, the quintic nonlinearity is dominant in the other family. Stability regions are identified by means of systematic numerical stability analysis. In the case of the first family, the size of the stability region increases up to moderate values of dispersive reflectivity. However for the second family (i.e. region where quintic nonlinearity dominates), the size of the stability region increases even for strong dispersive reflectivity. For all values of m, there exists a subset of the unstable solitons belonging to the first family for which the instability development leads to deformation and subsequent splitting of the soliton into two moving solitons with different amplitudes and velocities.
Musammil, N. M.; Porsezian, K.; Nithyanandan, K.; Subha, P. A.; Tchofo Dinda, P.
2017-09-01
We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.
Three-dimensional solutions in media with spatial dependence of nonlinear refractive index
International Nuclear Information System (INIS)
Kovachev, L.M.; Kaymakanova, N.I.; Dakova, D.Y.; Pavlov, L.I.; Donev, S.G.; Pavlov, R.L.
2004-01-01
We investigate a nonparaxial vector generalization of the scalar 3D+1 Nonlinear Schrodinger Equation (NSE). Exact analytical 3D+1 soliton solutions are obtained for the first time in media of spatial dependence of the nonlinear refractive index
Soliton on a cnoidal wave background in the coupled nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Shin, H J
2004-01-01
An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schroedinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new type of soliton solution in a self-focusing medium, which describes a breakup of a generalized dark-bright pair into another generalized dark-bright pair and an 'oscillating' soliton. We calculate the shift of the crest of the cnoidal wave along a soliton and the moving direction of the soliton on a cnoidal wave
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.
Qin, Yan-Hong; Zhao, Li-Chen; Yang, Zhan-Ying; Yang, Wen-Li
2018-01-01
We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by a pair-transition coupled two-component Bose-Einstein condensate. We demonstrate that the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark solitons, W-shaped solitons, multi-peak solitons, Kuznetsov-Ma like breathers, and multi-peak breathers. Specifically, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties. Furthermore, the interactions between these localized waves are discussed. The detailed analysis indicates that the soliton-soliton interaction induced phase shift brings the collision between these localized waves which can be inelastic for solitons involving collision and can be elastic for breathers. These characters come from the fact that the profile of solitons depends on the relative phase between bright solitons and a plane wave, and the profile of breathers does not depend on the relative phase. These results would motivate more discussions on linear interference between other nonlinear waves. Specifically, the solitons or breathers obtained here are not related to modulational instability. The underlying reasons are discussed in detail. In addition, possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.
Analytical study for the ability of nonlinear transmission lines to generate solitons
International Nuclear Information System (INIS)
Mostafa, S.I.
2009-01-01
The ability of the nonlinear transmission lines (NLTL) has been studied analytically, in this paper to generate solitons and to cause waveform spreading. This can be achieved by balancing nonlinearity and dispersion. A new technique of improved tanh method (ITM) and improved sech methods (ISM) is applied to the nonlinear partial differential equation that describes the NLTL. It is found that the parameters of the transmission line play an important role in controlling the shape of the soliton.
International Nuclear Information System (INIS)
Li Dejun; Mi Xianwu; 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 = j 0 .
Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.
Chowdury, A; Kedziora, D J; Ankiewicz, A; Akhmediev, N
2014-09-01
We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.
International Nuclear Information System (INIS)
Mahalingam, A; Porsezian, K; Mani Rajan, M S; Uthayakumar, A
2009-01-01
In this paper, a generalized nonlinear Schroedinger-Maxwell-Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Baecklund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed
Soliton Resolution for the Derivative Nonlinear Schrödinger Equation
Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine
2018-05-01
We study the derivative nonlinear Schrödinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the correction dispersive term. We use the nonlinear steepest descent method of Deift and Zhou (Commun Pure Appl Math 56:1029-1077, 2003) revisited by the {\\overline{partial}} -analysis of McLaughlin and Miller (IMRP Int Math Res Pap 48673:1-77, 2006) and Dieng and McLaughlin (Long-time asymptotics for the NLS equation via dbar methods. Preprint, arXiv:0805.2807, 2008), and complemented by the recent work of Borghese et al. (Ann Inst Henri Poincaré Anal Non Linéaire, https://doi.org/10.1016/j.anihpc.2017.08.006, 2017) on soliton resolution for the focusing nonlinear Schrödinger equation. Our results imply that N-soliton solutions of the derivative nonlinear Schrödinger equation are asymptotically stable.
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...
International Nuclear Information System (INIS)
Kono, M.; Kawakita, M.
1990-01-01
A nonlinear equation describing the development of the Buneman instability has been derived and solved with the aid of Hirota's bilinear transform [J. Math. Phys. 14, 810 (1973)] to give a variety of stationary solutions, such as pulsating solitons, temporally localized and spatially periodic solutions, as well as ordinary solitons
Molkenthin, Nora; Hu, Shuangwei; Niemi, Antti J.
2011-02-01
We introduce a novel generalization of the discrete nonlinear Schrödinger equation. It supports solitons that we utilize to model chiral polymers in the collapsed phase and, in particular, proteins in their native state. As an example we consider the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. We use its backbone as a template to explicitly construct a two-soliton configuration. Each of the two solitons describe well over 7.000 supersecondary structures of folded proteins in the Protein Data Bank with sub-angstrom accuracy suggesting that these solitons are common in nature.
Spatial optical (2+1)-dimensional scalar- and vector-solitons in saturable nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Weilnau, C.; Traeger, D.; Schroeder, J.; Denz, C. [Institute of Applied Physics, Westfaelische Wilhelms-Universitaet Muenster, Corrensstr. 2/4, 48149 Muenster (Germany); Ahles, M.; Petter, J. [Institute of Applied Physics, Technische Universitaet Darmstadt, Hochschulstr. 6, 64289 Darmstadt (Germany)
2002-10-01
(2+1)-dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton-supporting systems. Further on, we realize highly parallel, light-induced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all-optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi-component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle-light dualism of scalar solitons, various types of vector solitons can - in a broader sense - be interpreted as molecules of light. (Abstract Copyright [2002], Wiley Periodicals, Inc.)
Spatial optical (2+1)-dimensional scalar- and vector-solitons in saturable nonlinear media
International Nuclear Information System (INIS)
Weilnau, C.; Traeger, D.; Schroeder, J.; Denz, C.; Ahles, M.; Petter, J.
2002-01-01
(2+1)-dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton-supporting systems. Further on, we realize highly parallel, light-induced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all-optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi-component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle-light dualism of scalar solitons, various types of vector solitons can - in a broader sense - be interpreted as molecules of light. (Abstract Copyright [2002], Wiley Periodicals, Inc.)
Surface-wave solitons between linear media and nonlocal nonlinear media
International Nuclear Information System (INIS)
Shi Zhiwei; Li Huagang; Guo Qi
2011-01-01
We address surface solitons at the interface between linear media and nonlocal nonlinear media in the presence of a discontinuity in refractive index at the surface of these two materials. We investigated the influence of the degree of nonlocality on the stability, energy flow, and full width at half-maximum of the surface wave solitons. It is shown that surface solitons will be stable only if the degree of nonlocality exceeds a critical value. We find that the refractive index difference can affect the power distribution of the surface solitons in the two media. Also, different boundary values at the interface can lead to different relative peak positions of the surface solitons. However, neither the refractive index nor the boundary conditions can affect the stability of the solitons, for a given degree of nonlocality.
Brambila, Danilo; Fratalocchi, Andrea
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.
Stability of the static solitons in a pure spinor theory with fractional power nonlinearities
International Nuclear Information System (INIS)
Akdeniz, K.G.; Tezgor, G.; Barut, A.O.; Kalayci, J.; Okan, S.E.
1988-08-01
Soliton solutions are obtained in a pure fermionic model with fractional power nonlinear self-interactions. The stability properties of the minimum solutions have also been investigated within the framework of the Shatah-Strauss formalism. (author). 10 refs
International Nuclear Information System (INIS)
Pelinovsky, Dmitry E.; Yang Jianke
2005-01-01
We study the generalized third-order nonlinear Schroedinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons
All-fiber nonlinearity- and dispersion-managed dissipative soliton nanotube mode-locked laser
Energy Technology Data Exchange (ETDEWEB)
Zhang, Z. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Nanjing University of Posts and Communications, Nanjing 210003 (China); Popa, D., E-mail: dp387@cam.ac.uk; Wittwer, V. J.; Milana, S.; Hasan, T.; Jiang, Z.; Ferrari, A. C. [Cambridge Graphene Centre, University of Cambridge, Cambridge CB3 0FA (United Kingdom); Ilday, F. Ö. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Department of Electrical and Electronics Engineering, Bilkent University, 06800 Ankara (Turkey)
2015-12-14
We report dissipative soliton generation from an Yb-doped all-fiber nonlinearity- and dispersion-managed nanotube mode-locked laser. A simple all-fiber ring cavity exploits a photonic crystal fiber for both nonlinearity enhancement and dispersion compensation. The laser generates stable dissipative solitons with large linear chirp in the net normal dispersion regime. Pulses that are 8.7 ps long are externally compressed to 118 fs, outperforming current nanotube-based Yb-doped fiber laser designs.
Soliton formation at critical density in laser-irradiated plasmas
International Nuclear Information System (INIS)
Anderson, D.; Bondeson, A.; Lisak, M.
1979-01-01
The generation of Langmuir solitons at the resonance layer in a plasma irradiated by a strong high-frequency pump is investigated. The process is modelled by the nonlinear Schrodinger equation including an external pump, a density gradient and linear damping. The evolution equation is reformulated as an exact variational principle and the one-soliton generation process is studied by substituting various trial solutions. The applicability conditions for the nonlinear Schrodinger equation are re-examined and found to be more restrictive than previously stated. (author)
Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
ZHANG Yun-qiu; ZHANG Ning-chuan; PEI Yu-guo
2007-01-01
A numerical wave model based on the modified four-order nonlinear Schrodinger (NLS) equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is performed by changing sideband conditions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.
Exact optical solitons in (n + 1)-dimensions with anti-cubic nonlinearity
Younis, Muhammad; Shahid, Iram; Anbreen, Sumaira; Rizvi, Syed Tahir Raza
2018-02-01
The paper studies the propagation of optical solitons in (n + 1)-dimensions under anti-cubic law of nonlinearity. The bright, dark and singular optical solitons are extracted using the extended trial equation method. The constraint conditions, for the existence of these solitons, are also listed. Additionally, a couple of other solutions known as singular periodic and Jacobi elliptic solutions, fall out as a by-product of this scheme. The obtained results are new and reported first time in (n + 1)-dimensions with anti-cubic law of nonlinearity.
Guo, Boling; Wang, Yu-Feng; Liu, Nan
2018-01-01
This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics.
International Nuclear Information System (INIS)
Liu, Rong-Xiang; Tian, Bo; Liu, Li-Cai; Qin, Bo; Lü, Xing
2013-01-01
In this paper we investigate a fourth-order dispersive nonlinear Schrödinger equation, which governs the dynamics of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain with the octuple–dipole interaction in condensed-matter physics as well as the alpha helical proteins with higher-order excitations and interactions in biophysics. Beyond the existing constraint, upon the introduction of an auxiliary function, bilinear forms and N-soliton solutions are constructed with the Hirota method. Asymptotic analysis on the two-soliton solutions indicates that the soliton interactions are elastic. Soliton velocity varies linearly with the coefficient of discreteness and higher-order magnetic interactions. Bound-state solitons can also exist under certain conditions. Period of a bound-state soliton is inversely correlated to the coefficient of discreteness and higher-order magnetic interactions. Interactions among the three solitons are all pairwise elastic
Non-linear Evolution of the Transverse Instability of Plane-Envelope Solitons
DEFF Research Database (Denmark)
Janssen, Peter A. E. M.; Juul Rasmussen, Jens
1983-01-01
The nonlinear evolution of the transverse instability of plane envelope soliton solutions of the nonlinear Schrödinger equation is investigated. For the case where the spatial derivatives in the two‐dimensional nonlinear Schrödinger equation are elliptic a critical transverse wavenumber is found...
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.
Optical soliton solutions for two coupled nonlinear Schroedinger systems via Darboux transformation
International Nuclear Information System (INIS)
Zhang Haiqiang; Li Juan; Xu Tao; Zhang Yaxing; Hu Wei; Tian Bo
2007-01-01
In nonlinear optical fibers, the vector solitons can be governed by the systems of coupled nonlinear Schroedinger from polarized optical waves in an isotropic medium. Based on the Ablowitz-Kaup-Newell-Segur technology, the Darboux transformation method is successfully applied to two coupled nonlinear Schroedinger systems. With the help of symbolic computation, the bright vector one- and two-soliton solutions including one-peak and two-peak solitons are further constructed via the iterative algorithm of Darboux transformation. Through the figures for several sample solutions, the stable propagation and elastic collisions for these kinds of bright vector solitons are discussed and the possible applications are pointed out in optical communications and relevant optical experiments.In addition, the conserved quantities of such two systems, i.e., the energy, momentum and Hamiltonian, are also presented
International Nuclear Information System (INIS)
Chen Qianyong; Kevrekidis, Panayotis G; Malomed, Boris A
2012-01-01
We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schrödinger equation, which includes the harmonic oscillator 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 a BEC. The 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. The main features of these dependences are explained qualitatively. (paper)
International Nuclear Information System (INIS)
Shi, Zhiwei; Li, Huagang; Guo, Qi
2012-01-01
We address multipole surface solitons occurring at the interface between a linear medium and a nonlocal nonlinear medium. We show the impact of nonlocality, the propagation constant, and the linear index difference of two media on the properties of the surface solitons. We find that there exist a threshold value of the degree of the nonlocality at the same linear index difference of two media, only when the degree of the nonlocality goes beyond the value, the multipole surface solitons can be stable. -- Highlights: ► We show the impact of nonlocality and the linear index difference of two media on the properties of the surface solitons. ► For the surface solitons, only when the degree of the nonlocality goes beyond a threshold value, they can be stable. ► The number of poles and the index difference of two media can all influence the threshold value.
International Nuclear Information System (INIS)
Ventura, J.
1983-01-01
An introductory and partial discussion on the conceptual news and the multiple consequences which originate from the existence of solitons is presented. Preliminary calculations related with the helium superfluid theory are discussed. (L.C.) [pt
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
in contrast to a recently found azimuthal instability of spinning doughnut-shaped solitons in the CQ NLS equation, their GL counterparts may be completely stable. On the other hand, a problem of fundamental interest is the possibility of the formation of fully three-dimensional (3D) optical spatiotemporal solitons, also referred ...
Pure soliton solutions of some nonlinear partial differential equations
International Nuclear Information System (INIS)
Fuchssteiner, B.
1977-01-01
A general approach is given to obtain the system of ordinary differential equations which determines the pure soliton solutions for the class of generalized Korteweg-de Vries equations. This approach also leads to a system of ordinary differential equations for the pure soliton solutions of the sine-Gordon equation. (orig.) [de
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.
Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.
Porras, Miguel A; Ramos, Francisco
2017-09-01
The applications of vortex solitons are severely limited by the diffraction and self-defocusing spreading of the background beam where they are nested. Nonlinear Bessel beams in self-defocusing media are nondiffracting, flattop beams where the nested vortex solitons can survive for propagation distances that are one order of magnitude larger than in the Gaussian or super-Gaussian beams. The dynamics of the vortex solitons is studied numerically and found to approach that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.
Polariton solitons and nonlinear localized states in a one-dimensional semiconductor microcavity
Chen, Ting-Wei; Cheng, Szu-Cheng
2018-01-01
This paper presents numerical studies of cavity polariton solitons (CPSs) in a resonantly pumped semiconductor microcavity with an imbedded spatial defect. In the bistable regime of the well-known homogeneous polariton condensate, with proper incident wave vector and pump strength, bright and/or dark cavity solitons can be found in the presence of a spatially confined potential. The minimum pump strength required to observe the CPSs or nonlinear localized states in this parametric pump scheme is therefore reported.
International Nuclear Information System (INIS)
Khrennikov, A.
2005-01-01
We constructed the representation of contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function can be considered as Hilbert space projection of realistic dynamics in a pre space. The basic condition for representing the pre space-dynamics is the law of statistical conservation of energy-conservation of probabilities. The construction of the dynamical representation is an important step in the development of contextual statistical viewpoint of quantum processes. But the contextual statistical model is essentially more general than the quantum one. Therefore in general the Hilbert space projection of the pre space dynamics can be nonlinear and even irreversible (but it is always unitary). There were found conditions of linearity and reversibility of the Hilbert space dynamical projection. We also found conditions for the conventional Schrodinger dynamics (including time-dependent Hamiltonians). We remark that in general even the Schrodinger dynamics is based just on the statistical conservation of energy; for individual systems the law of conservation of energy can be violated (at least in our theoretical model)
Facão, M.; Carvalho, M. I.
2017-10-01
In this work, we present parameter regions for the existence of stable plain solitons of the cubic complex Ginzburg-Landau equation (CGLE) with higher-order terms associated with a fourth-order expansion. Using a perturbation approach around the nonlinear Schrödinger equation soliton and a full numerical analysis that solves an ordinary differential equation for the soliton profiles and using the Evans method in the search for unstable eigenvalues, we have found that the minimum equation allowing these stable solitons is the cubic CGLE plus a term known in optics as Raman-delayed response, which is responsible for the redshift of the spectrum. The other favorable term for the occurrence of stable solitons is a term that represents the increase of nonlinear gain with higher frequencies. At the stability boundary, a bifurcation occurs giving rise to stable oscillatory solitons for higher values of the nonlinear gain. These oscillations can have very high amplitudes, with the pulse energy changing more than two orders of magnitude in a period, and they can even exhibit more complex dynamics such as period-doubling.
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.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education. Erwin Schrodinger. Articles written in Resonance – Journal of Science Education. Volume 4 Issue 2 February 1999 pp 92-103 Classics. The Fundamental Idea of Wave Mechanics · Erwin Schrodinger · More Details Fulltext PDF ...
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.
Crosta, M.; Fratalocchi, Andrea; Trillo, S.
2011-01-01
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.
A real nonlinear integrable couplings of continuous soliton hierarchy and its Hamiltonian structure
International Nuclear Information System (INIS)
Yu Fajun
2011-01-01
Some integrable coupling systems of existing papers are linear integrable couplings. In the Letter, beginning with Lax pairs from special non-semisimple matrix Lie algebras, we establish a scheme for constructing real nonlinear integrable couplings of continuous soliton hierarchy. A direct application to the AKNS spectral problem leads to a novel nonlinear integrable couplings, then we consider the Hamiltonian structures of nonlinear integrable couplings of AKNS hierarchy with the component-trace identity. - Highlights: → We establish a scheme to construct real nonlinear integrable couplings. → We obtain a novel nonlinear integrable couplings of AKNS hierarchy. → Hamiltonian structure of nonlinear integrable couplings AKNS hierarchy is presented.
Glimpses of soliton theory the algebra and geometry of nonlinear PDEs
Kasman, Alex
2010-01-01
Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstr...
Nonlinear Schrodinger elliptic systems involving exponential critical growth in R^2
Directory of Open Access Journals (Sweden)
Francisco S. B. Albuquerque Albuquerque
2014-02-01
Full Text Available This article concerns the existence and multiplicity of solutions for elliptic systems with weights, and nonlinearities having exponential critical growth. Our approach is based on the Trudinger-Moser inequality and on a minimax theorem.
International Nuclear Information System (INIS)
Abe, H.; Okuda, H.
1994-06-01
Soliton propagation in the dielectric media has been simulated by using the nonlinear Lorentz computational model, which was recently developed to study the propagation of electromagnetic waves in a linear and a nonlinear dielectric. The model is constructed by combining a microscopic model used in the semi-classical approximation for dielectric media and the particle model developed for the plasma simulations. The carrier wave frequency is retained in the simulation so that not only the envelope of the soliton but also its phase can be followed in time. It is shown that the model may be useful for studying pulse propagation in the dielectric media
Scattering of quantized solitary waves in the cubic Schrodinger equation
International Nuclear Information System (INIS)
Dolan, L.
1976-01-01
The quantum mechanics for N particles interacting via a delta-function potential in one space dimension and one time dimension is known. The second-quantized description of this system has for its Euler-Lagrange equations of motion the cubic Schrodinger equation. This nonlinear differential equation supports solitary wave solutions. A quantization of these solitons reproduces the weak-coupling limit to the known quantum mechanics. The phase shift for two-body scattering and the energy of the N-body bound state is derived in this approximation. The nonlinear Schrodinger equation is contrasted with the sine-Gordon theory in respect to the ideas which the classical solutions play in the description of the quantum states
Dissipative Vortex Solitons in Defocusing Media with Spatially Inhomogeneous Nonlinear Absorption
Lai, Xian-Jing; Cai, Xiao-Ou; Zhang, Jie-Fang
2018-02-01
In this paper, by solving a complex nonlinear Schrödinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonlinear absorption gives rise to the stability of dissipative vortex solitons in self-defocusing nonlinear medium in the presence of constant linear gain. Numerical simulation reveals the interaction effect among linear gain and nonlinear loss in the azimuthal modulation instabilities of these vortices suppression. Apart from the uniform linear gain indeed affects the stability of vortex in this media, another noticeable feature of current setup is that the steep spatial modulation of the nonlinear absorption can suppress sidelobes effectively and support stable vortex solitons in situations with uniform linear gain. Under appropriate conditions, the vortex solitons can propagate stably and feature no symmetry breaking, although the beams exhibit radical compression and amplification as they propagate. Supported by the National Natural Science Foundation of China under Grant No. 11705164 and the Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ16A040003
Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method
Directory of Open Access Journals (Sweden)
Hassan A. Zedan
2012-01-01
Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.
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.
International Nuclear Information System (INIS)
Dai, Chao-Qing; Qin, Zhen-Yun; Zheng, Chun-Long
2012-01-01
Multi-soliton solutions to the modified nonlinear Schrödinger equation (MNLSE) with variable coefficients (VCs) in inhomogeneous fibers are obtained with the help of mapping transformation, which reduces the VC MNLSE into a constant-coefficient MNLSE. Based on the analytical solutions, one- and two-soliton transmissions in the proper dispersion management systems are discussed. The sustainment of solitons and the disappearance of breathers for the VC MNLSE are first reported here. (paper)
International Nuclear Information System (INIS)
Xu Guiqiong; Li Zhibin
2005-01-01
It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests
On the reflection of solitons of the cubic nonlinear Schrödinger equation
Katsaounis, Theodoros; Mitsotakis, Dimitrios
2016-01-01
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
Modelling of the nonlinear soliton dynamics in the ring fibre cavity
Razukov, Vadim A.; Melnikov, Leonid A.
2018-04-01
Using the cabaret method numerical realization, long-time spatio-temporal dynamics of the electromagnetic field in a nonlinear ring fibre cavity with dispersion is investigated during the hundreds of round trips. Formation of both the temporal cavity solitons and irregular pulse trains is demonstrated and discussed.
Singular solitons and other solutions to a couple of nonlinear wave equations
International Nuclear Information System (INIS)
Inc Mustafa; Ulutaş Esma; Biswas Anjan
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
Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.
2010-09-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
International Nuclear Information System (INIS)
Zhang Jiefang; Meng Jianping; Wu Lei; Li Yishen; Malomed, Boris A.
2010-01-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
Upper-hybrid solitons and oscillating-two-stream instabilities
International Nuclear Information System (INIS)
Porkolab, M.; Goldman, M.V.
1976-01-01
A warm two-fluid theory of soliton formation near the upper-hybrid frequency is developed. Several forms of the nonlinear Schrodinger equation are obtained, depending on whether the electric field is completely perpendicular to the dc magnetic field or whether it has an additional small component parallel to the magnetic field. For the perpendicular case, the character of the soliton depends on its scale length, L, and on β. For low β, when L c/ω/subp//subi/ the super-Alvenic solitons described magnetohydromagnetically by Kaufman and Stenflo are obtained. However, the case E/sub parallel/not-equal0 may be of more interest, since it couples the pump to the excited waves more efficiently. In the limit of linearization about an infinite wavelength pump, the nonlinear Schrodinger equations yield purely growing (oscillating-two-stream) instabilities in both cases
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.
Nonlinear ion-acoustic waves and solitons in a magnetized plasma
International Nuclear Information System (INIS)
Lee, L.C.; Kan, J.R.
1981-01-01
A unified formulation is presented to study the nonlinear low-frequency electrostatic waves in a magnetized low-β plasma. It is found that there exist three types of nonlinear waves; (1) nonlinear ion-cyclotron periodic waves with a wave speed V/sub p/ > C/sub s/ (ion-acoustic velocity); (2) nonlinear ion-acoustic periodic waves with V/sub p/ < C/sub s/ costheta; and (3) ion-acoustic solitons with C/sub s/ costheta < V/sub p/ < C/sub s/, where theta is the angle between the wave vector and the magnetic field
Fujishima, Hironobu; Okumura, Masahiko; Mine, Makoto; Yajima, Tetsu
2012-01-01
We propose an indirect method to observe radiation from an incomplete soliton with sufficiently large amplitude. We show that the radiation causes a notched structure on the envelope of the wave packet in the momentum space. The origin of this structure is a result of interference between the main body of oscillating solitons and the small radiation in the momentum space. We numerically integrate the nonlinear Schr\\"odinger equation and perform Fourier transformation to confirm that the predi...
Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan
2018-01-01
We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.
Institute of Scientific and Technical Information of China (English)
ZHANG RongPei; YU XiJun; LI MingJun; LI XiangGui
2017-01-01
In this study,we present a conservative local discontinuous Galerkin (LDG) method for numerically solving the two-dimensional nonlinear Schr(o)dinger (NLS) equation.The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux.The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central,alternative and upwind-based flux.We will propose two kinds of time discretization methods for the semi-discrete formulation.One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation.The other one is Krylov implicit integration factor (ⅡF) method which demands much less computational effort.Various numerical experiments are presented to demonstrate the conservation law of mass and energy,the optimal rates of convergence,and the blow-up phenomenon.
DEFF Research Database (Denmark)
Zeng, Xianglong; Guo, Hairun; Zhou, Binbin
2012-01-01
We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression...... with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest...... soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency...
International Nuclear Information System (INIS)
Wu Jianping
2010-01-01
Based on the Hirota bilinear form, a simple approach without employing the standard perturbation technique, is presented for constructing a novel N-soliton solution for a (3+1)-dimensional nonlinear evolution equation. Moreover, the novel N-soliton solution is shown to have resonant behavior with the aid of Mathematica. (general)
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
International Nuclear Information System (INIS)
Luz, H. L. F. da; Gammal, A.; Abdullaev, F. Kh.; Salerno, M.; Tomio, Lauro
2010-01-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro
2010-10-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
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.
International Nuclear Information System (INIS)
Zhang, Yu-Juan; Zhao, Dun; Luo, Hong-Gang
2014-01-01
We consider a wide class of integrable nonautonomous nonlinear integro-differential Schrödinger equation which contains the models for the soliton management in Bose–Einstein condensates, nonlinear optics, and inhomogeneous Heisenberg spin chain. With the help of the nonisospectral AKNS hierarchy, we obtain the N-fold Darboux transformation and the N-fold soliton-like solutions for the equation. The soliton management, especially the synchronized dispersive and nonlinear management in optical fibers is discussed. It is found that in the situation without external potential, the synchronized dispersive and nonlinear management can keep the integrability of the nonlinear Schrödinger equation; this suggests that in optical fibers, the synchronized dispersive and nonlinear management can control and maintain the propagation of a multi-soliton. - Highlights: • We consider a unified model for soliton management by an integrable integro-differential Schrödinger equation. • Using Lax pair, the N-fold Darboux transformation for the equation is presented. • The multi-soliton management is considered. • The synchronized dispersive and nonlinear management is suggested
Cross-talk dynamics of optical solitons in a broadband Kerr nonlinear system with weak cubic loss
International Nuclear Information System (INIS)
Peleg, Avner; Nguyen, Quan M.; Chung, Yeojin
2010-01-01
We study the dynamics of fast soliton collisions in a Kerr nonlinear optical waveguide with weak cubic loss. We obtain analytic expressions for the amplitude and frequency shifts in a single two-soliton collision and show that the impact of a fast three-soliton collision is given by the sum of the two-soliton interactions. Our analytic predictions are confirmed by numerical simulations with the perturbed nonlinear Schroedinger (NLS) equation. Furthermore, we show that the deterministic collision-induced dynamics of soliton amplitudes in a broadband waveguide system with N frequency channels is described by a Lotka-Volterra model for N competing species. For a two-channel system we find that stable transmission with equal prescribed amplitudes can be achieved by a proper choice of linear amplifier gain. The predictions of the Lotka-Volterra model are confirmed by numerical solution of a perturbed coupled-NLS model.
On modelling adiabatic N-soliton interactions and perturbations. Effects of external potentials
International Nuclear Information System (INIS)
Gerdjikov, V.; Baizakov, B.
2005-01-01
We analyze several perturbed versions of the complex Toda chain (CTC) in an attempt to describe the adiabatic N-soliton train interactions of the perturbed nonlinear Schrodinger equation (NLS). Particular types of perturbations, including quadratic and periodic external potentials are treated by both analytical and numerical means. We show that the perturbed CTC model provides a good description for the N-soliton interactions in the presence of a weak external potential. (authors)
Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.
2010-01-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite number of exact soliton solutions in terms of the Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite bandgap of the optical-lattice-induced spectrum. Starting from the exact solutions, we employ the relaxation met...
International Nuclear Information System (INIS)
Biswas, Anjan
2009-01-01
In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.
International Nuclear Information System (INIS)
Konar, S.; Mishra, Manoj; Jana, S.
2006-01-01
The role of quintic nonlinearity on the propagation characteristics of optical solitons in dispersion managed optical communication systems has been presented in this paper. It has been shown that quintic nonlinearity has only marginal influence on single pulse propagation. However, numerical simulation has been undertaken to reveal that quintic nonlinearity reduces collision distance between neighbouring pulses of the same channel. It is found that for lower map strength the collapse distance between intra channel pulses is very much sensitive to the dispersion map strength
International Nuclear Information System (INIS)
Wang Lei; Zhu Yujie; Wang Ziqi; Xu Tao; Qi Fenghua; Xue Yushan
2016-01-01
We study the nonlinear localized waves on constant backgrounds of the Hirota–Maxwell–Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons. (author)
Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan
2016-02-01
We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.
Nonlinear excitations in two-dimensional molecular structures with impurities
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth
1995-01-01
We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence...... of the impurity. Transforming the equation to the noninertial frame of reference coupled with the center of mass we investigate the soliton behavior in the close vicinity of the impurity. With the help of the lens transformation we show that the soliton width is governed by an Ermakov-Pinney equation. We also...... excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation....
Inelastic collision of two solitons for generalized BBM equation with cubic nonlinearity
Directory of Open Access Journals (Sweden)
Jingdong Wei
2015-06-01
Full Text Available We study the inelastic collision of two solitary waves of different velocities for the generalized Benjamin-Bona-Mahony (BBM equation with cubic nonlinearity. It shows that one solitary wave is smaller than the other one in the H^1(R energy space. We explore the sharp estimates of the nonzero residue due to the collision, and prove the inelastic collision of two solitary waves and nonexistence of a pure 2-soliton solution.
Solitons of scalar field with induced nonlinearity and their stability
International Nuclear Information System (INIS)
Saha, B.
1999-09-01
Exact particle-like static, spherically and/or cylindrically symmetric solutions to the equations of interacting scalar and electromagnetic field system have been obtained. We considered FRW and Goedel universes as external gravitational field with spherical and cylindrical symmetry respectively. Beside the usual solitons some special regular solutions known as droplets, anti-droplets and hats (confined in finite interval and having trivial value beyond it) have been obtained. It has been shown that in FRW space-time equations with different interaction terms may have stable solutions while within the scope of Goedel model only the droplet-like and the hat-like configurations may be stable, providing that they are located in the region where g 00 > 0. (author)
Self-focusing instability of two-dimensional solitons and vortices
DEFF Research Database (Denmark)
Kuznetsov, E.A.; Juul Rasmussen, J.
1995-01-01
The instability of two-dimensional solitons and vortices is demonstrated in the framework of the three-dimensional nonlinear Schrodinger equation (NLSE). The instability can be regarded as the analog of the Kadomtsev-Petviashvili instability [B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl...
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric and have a positive definite Fourier spectrum, but can otherwise be of completely arbitrary shape and degree of nonlocality...
Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality
International Nuclear Information System (INIS)
Dai, Zhiping; Yang, Zhenjun; Ling, Xiaohui; Zhang, Shumin; Pang, Zhaoguang
2016-01-01
The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and the oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.
Soliton solution for nonlinear partial differential equations by cosine-function method
International Nuclear Information System (INIS)
Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.
2007-01-01
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-sustained solitons in systems with nonlinear damping
International Nuclear Information System (INIS)
Gonzalez, J.A.
1993-05-01
The existence and stability of kinks in systems with nonlinear damping are investigated. We discuss the mechanism of a bifurcation after which the kink becomes a non-stationary state. (author). 9 refs
International Nuclear Information System (INIS)
Kavitha, L.; Daniel, M.
2002-07-01
The integrability of one dimensional classical continuum inhomogeneous biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity on the soliton of an underlying completely integrable spin model are studied. The dynamics of the spin system is expressed in terms of a higher order generalized nonlinear Schroedinger equation through a differential geometric approach which becomes integrable for a particular choice of the biquadratic exchange interaction and for linear inhomogeneity. The effect of nonlinear inhomogeneity on the spin soliton is studied by carrying out a multiple scale perturbation analysis. (author)
Strong phase correlations of solitons of nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Litvak, A.G.; Mironov, V.A.; Protogenov, A.P.
1994-06-01
We discuss the possibility to suppress the collapse in the nonlinear 2+1 D Schroedinger equation by using the gauge theory of strong phase correlations. It is shown that invariance relative to q-deformed Hopf algebra with deformation parameter q being the fourth root of unity makes the values of the Chern-Simons term coefficient, k=2, and of the coupling constant, g=1/2, fixed; no collapsing solutions are present at those values. (author). 21 refs
Bright and dark soliton solutions for some nonlinear fractional differential equations
International Nuclear Information System (INIS)
Guner, Ozkan; Bekir, Ahmet
2016-01-01
In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space–time fractional modified Benjamin–Bona–Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann–Liouville sense. (paper)
Nonlinear quantum piston for the controlled generation of vortex rings and soliton trains
Pinsker, Florian; Berloff, Natalia G.; Pé rez-Garcí a, Ví ctor M.
2013-01-01
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.
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.
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
phase shifts accessible. This self-defocusing nonlinearity can be used to compress a pulse when combined with normal dispersion, and problems normally encountered due to self-focusing in cubic media are avoided. Thus, having no power limit, in bulk media a self-defocusing soliton compressor can create...... high-energy near single-cycle fs pulses (Liu et al., 2006). However, the group-velocity mismatch (GVM) between the FW and second harmonic (SH), given by the inverse group velocity difference d12=1/Vg,1 - 1/Vg,2, limits the pulse quality and compression ratio. Especially very short input pulses (...
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.
Interaction of solitons with a string of coupled quantum dots
Energy Technology Data Exchange (ETDEWEB)
Kumar, Vijendra, E-mail: vsmedphysics@gmail.com; Swami, O. P., E-mail: omg1789@gmail.com; Nagar, A. K., E-mail: ajaya.nagar@gmail.com [Department of Physics, Govt. Dungar College, Bikaner, Rajasthan 334001 (India); Taneja, S., E-mail: sachintaneja9@gmail.com [Department of Radiotherapy, CHAF Bangalore, Karnataka 560007 (India)
2016-05-06
In this paper, we develop a theory for discrete solitons interaction with a string of coupled quantum dots in view of the local field effects. Discrete nonlinear Schrodinger (DNLS) equations are used to describe the dynamics of the string. Numerical calculations are carried out and results are analyzed with the help of matlab software. With the help of numerical solutions we demonstrate that in the quantum dots string, Rabi oscillations (RO) are self trapped into stable bright Rabi solitons. The Rabi oscillations in different types of nanostructures have potential applications to the elements of quantum logic and quantum memory.
Energy Technology Data Exchange (ETDEWEB)
Han, Jiu-Ning, E-mail: hanjiuning@126.com; Luo, Jun-Hua; Li, Jun-Xiu [Institute of Theoretical Physics and College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China); Li, Sheng-Chang [School of Science, Xi' an Jiaotong University, Xi' an 710049 (China); Liu, Shi-Wei; Yang, Yang; Duan, Wen-Shan; Han, Juan-Fang [Joint Laboratory of Atomic and Molecular Physics of NWNU and IMPCAS and College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070 (China)
2015-06-15
We study the basic physical properties of composite nonlinear structure induced by the head-on collision of magnetosonic solitons. Solitary waves are assumed to propagate in a quantum electron-ion magnetoplasma with spin-1/2 degenerate electrons. The main interest of the present work is to investigate the time evolution of the merged composite structure during a specific time interval of the wave interaction process. We consider three cases of colliding-situation, namely, compressive-rarefactive solitons interaction, compressive-compressive solitons interaction, and rarefactive-rarefactive solitons interaction, respectively. Compared with the last two colliding cases, the changing process of the composite structure is more complex for the first situation. Moreover, it is found that they are obviously different for the last two colliding cases.
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices
International Nuclear Information System (INIS)
Carusotto, Iacopo; Embriaco, Davide; La Rocca, Giuseppe C.
2002-01-01
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties
International Nuclear Information System (INIS)
Sun Zhiyuan; Yu Xin; Liu Ying; Gao Yitian
2012-01-01
We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.
Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying
2012-12-01
We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.
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
Blas, H.; do Bonfim, A. C. R.; Vilela, A. M.
2017-05-01
Deformations of the focusing non-linear Schrödinger model (NLS) are considered in the context of the quasi-integrability concept. We strengthen the results of JHEP 09 (2012) 103 10.1007/JHEP06(2015)177" TargetType="URL"/> for bright soliton collisions. We addressed the focusing NLS as a complement to the one in JHEP 03 (2016) 005 10.1007/JHEP06(2015)177" TargetType="URL"/> , 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=2η /2+\\upepsilon{({|ψ |}^2)}^{2+\\upepsilon},\\upepsilon \\in \\mathbb{R},η <0 . However, for two-soliton field components without definite parity we also show numerically the vanishing of the first non-trivial anomaly and the exact conservation of the relevant charge. So, the parity symmetry seems to be a sufficient but not a necessary condition for the existence of the infinite tower of conserved charges. The model supports elastic scattering of solitons for a wide range of values of the amplitudes and velocities and the set { η, ɛ}. Since the NLS equation is ubiquitous, our results may find potential applications in several areas of non-linear science.
Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen
2017-12-01
In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.
Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman
2015-04-01
The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.
Observation of ion acoustic multi-Peregrine solitons in multicomponent plasma with negative ions
Pathak, Pallabi; Sharma, Sumita K.; Nakamura, Y.; Bailung, H.
2017-12-01
The evolution of the multi-Peregrine soliton is investigated in a multicomponent plasma and found to be critically dependent on the initial bound state. Formation and splitting of Peregrine soliton, broadening of the frequency spectra provide clear evidence of nonlinear-dispersive focusing due to modulational instability, a generic mechanism for rogue wave formation in which amplitude and phase modulation grow as a result of interplay between nonlinearity and anomalous dispersion. We have shown that initial perturbation parameters (amplitude & temporal length) critically determine the number of solitons evolution. It is also found that a sufficiently long wavelength perturbation of high amplitude invoke strong nonlinearity to generate a supercontinuum state. Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) analysis of the experimental time series data clearly indicate the spatio-temporal localization and spectral broadening. We consider a model based on the frame work of Nonlinear Schrodinger equation (NLSE) to explain the experimental observations.
Li, Ming-Zhen; Tian, Bo; Qu, Qi-Xing; Chai, Han-Peng; Liu, Lei; Du, Zhong
2017-12-01
In this paper, under investigation is a coupled variable-coefficient higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the Lax pair and binary Darboux transformation, we present the nondegenerate N-dark-dark soliton solutions. With the graphical simulation, soliton propagation and interaction are discussed with the group velocity dispersion and fourth-order dispersion effects, which affect the velocity but have no effect on the amplitude. Linear, parabolic and periodic one dark-dark solitons are displayed. Interactions between the two solitons are presented as well, which are all elastic.
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.
Chen, Yong; Yan, Zhenya
2016-03-22
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.
Soliton-based ultrafast multi-wavelength nonlinear switching in dual-core photonic crystal fibre
International Nuclear Information System (INIS)
Stajanca, P; Pysz, D; Michalka, M; Bugar, I; Andriukaitis, G; Balciunas, T; Fan, G; Baltuska, A
2014-01-01
Systematic experimental study of ultrafast multi-wavelength all-optical switching performance in a dual-core photonic crystal fibre is presented. The focus is on nonlinearly induced switching between the two output ports at non-excitation wavelengths, which are generated during nonlinear propagation of femtosecond pulses in the anomalous dispersion region of a dual-core photonic crystal fibre made of multicomponent glass. Spatial and spectral characteristics of the fibre output radiation were measured separately for both fibre cores under various polarization and intensity conditions upon selective, individual excitation of each fibre core. Polarization-controlled nonlinear switching performance at multiple non-excitation wavelengths was demonstrated in the long-wavelength optical communication bands and beyond. Depending on the input pulse polarization, narrowband switching operation at 1560 nm and 1730 nm takes place with double core extinction ratio contrasts of 9 dB and 14.5 dB, respectively. Moreover, our approach allows switching with simultaneous wavelength shift from 1650 to 1775 nm with extinction ratio contrast larger than 18 dB. In addition, non-reciprocal behaviour of the soliton fission process under different fibre core excitations was observed and its effect on the multi-wavelength nonlinear switching performance was explained, taking into account the slight dual-core structure asymmetry. The obtained results represent ultrafast all-optical switching with an extended dimension of wavelength shift, controllable with both the input radiation intensity and the polarization by simple propagation along a 14 mm long fibre. (paper)
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.
Soliton-soliton effective interaction
International Nuclear Information System (INIS)
Maki, J.N.
1986-01-01
A scheme of semi-phenomenological quantization is proposed for the collision process of two equal size envelopes-solitons provided by nonlinear Schroedinger equation. The time advance due to two envelopes-solitons collision was determined. Considering the solitons as puntual particles and using the description of classical mechanics, the effective envelope soliton-envelope soliton attractive potential, denominated modified Poschl-Teller potential. The obtainment of this potential was possible using the information in from of system memory, done by an analytical expression of time delay. Such system was quantized using this effective potential in Schroeding equation. The S col matrix of two punctual bodies was determined, and it is shown that, in the limit of 1 2 2 /mN 4 it reproduces the exact S 2N matrix obtained from soliton packet wich incurs on another soliton packet. Every ones have the same mass, interacts by contact force between two bodies. These packets have only one bound state, i e, do not have excited states. It was verified that, using the S col matrix, the binding energy of ground state of the system can be obtained, which is coincident with 2N particles in the 1/N approximation. In this scheme infinite spurious bound states are found (M.C.K.) [pt
Nonlinear dynamics of a soliton gas: Modified Korteweg–de Vries equation framework
Energy Technology Data Exchange (ETDEWEB)
Shurgalina, E.G., E-mail: eshurgalina@mail.ru [Department of Nonlinear Geophysical Processes, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Pelinovsky, E.N. [Department of Nonlinear Geophysical Processes, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Department of Applied Mathematics, Nizhny Novgorod State Technical University, Nizhny Novgorod (Russian Federation)
2016-05-27
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.
Su, Jing-Jing; Gao, Yi-Tian
2018-03-01
Under investigation in this paper is a higher-order nonlinear Schrödinger equation with space-dependent coefficients, related to an optical fiber. Based on the self-similarity transformation and Hirota method, related to the integrability, the N-th-order bright and dark soliton solutions are derived under certain constraints. It is revealed that the velocities and trajectories of the solitons are both affected by the coefficient of the sixth-order dispersion term while the amplitudes of the solitons are determined by the gain function. Amplitudes increase when the gain function is positive and decrease when the gain function is negative. Furthermore, we find that the intensities of dark solitons are presented as a superposition of the solitons and stationary waves.
International Nuclear Information System (INIS)
Yomba, Emmanuel
2008-01-01
With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons
The nonlinear evolution of ring dark solitons in Bose-Einstein condensates
International Nuclear Information System (INIS)
Xue Jukui
2004-01-01
The dynamics of the ring dark soliton in a Bose-Einstein condensate (BEC) with thin disc-shaped potential is investigated analytically and numerically. Analytical investigation shows that the ring dark soliton in the radial non-symmetric cylindrical BEC is governed by a cylindrical Kadomtsev-Petviashvili equation, while the ring dark soliton in the radial symmetric cylindrical BEC is governed by a cylindrical Korteweg-de Vries equation. The reduction to the cylindrical KP or KdV equation may be useful to understand the dynamics of a ring dark soliton. The numerical results show that the evolution properties and the snaking of a ring dark soliton are modified significantly by the trapping
International Nuclear Information System (INIS)
Wang, Pan; Tian, Bo; Jiang, Yan; Wang, Yu-Feng
2013-01-01
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
Energy Technology Data Exchange (ETDEWEB)
Abram, I [Centre National d' Etudes des Telecommunications (CNET), 196 Avenue Henri Ravera, F-92220 Bagneux (France)
1999-02-01
Two of the most remarkable properties of light - squeezing and solitons - are being combined in a new generation of experiments that could revolutionize optics and communications. One area of application concerns the transmission and processing of classical (binary) information, in which the presence or absence of a soliton in a time-window corresponds to a ''1'' or ''0'', as in traditional optical-fibre communications. However, since solitons occur at fixed power levels, we do not have the luxury of being able to crank up the input power to improve the signal-to-noise ratio at the receiving end. Nevertheless, the exploitation of quantum effects such as squeezing could help to reduce noise and improve fidelity. In long-distance communications, where the signal is amplified every 50-100 kilometres or so, the soliton pulse is strongest just after the amplifier. Luckily this is where the bulk of the nonlinear interaction needed to maintain the soliton shape occurs. However, the pulse gets weaker as it propagates along the fibre, so the nonlinear interaction also becomes weakerand weaker. This means that dispersive effects become dominant until the next stage of amplification, where the nonlinearity takes over again. One problem is that quantum fluctuations in the amplifiers lead to random jumps in the central wavelength of the individual solitons, and this results in a random variation of the speed of individual solitons in the fibre. Several schemes have been devised to remove this excess noise and bring the train of solitons back to the orderly behaviour characteristic of a stable coherent state (e.g. the solitons could be passed through a spectral filter). Photon-number squeezing could also play a key role in solving this problem. For example, if the solitons are number-squeezed immediately after amplification, there will be a smaller uncertainty in the nonlinearity that keeps the soliton in shape and, therefore, there will also be less noise in the soliton. This
Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian
2018-01-01
In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.
Hydrodynamic optical soliton tunneling
Sprenger, P.; Hoefer, M. A.; El, G. A.
2018-03-01
A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.
Cuevas-Maraver, J.; Malomed, Boris A.; Kevrekidis, P. G.; Frantzeskakis, D. J.
2018-04-01
We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) self-defocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.
The nonlinear Fourier analysis of internal solitons in the Andaman sea
International Nuclear Information System (INIS)
Osborne, A.R.; Provenzale, A.; Bergamasco, L.
1983-01-01
A preliminary spectral analysis of large-amplitude internal solitons in the Andaman Sea was conducted, employing method based upon the spectral (or scattering) transform solution of the Korteweg-de Vries equation
Nonlinear localized excitations in magnets with a weak exchange interaction as a soliton problem
International Nuclear Information System (INIS)
Gvozdikova, M.V.; Kovalev, A.S.
1998-01-01
The spin dynamics of soliton-like localized excitations in a discrete ferromagnet chain with an easy axis anisotropy and a weak exchange interaction is studied. The connection of these excitations with longwave magnetic solitons is discussed. The localized excitation frequency dependence on exchange interaction is found for a fixed number of spin deviation. It is shown that this dependence modifies essentially when the exchange interaction becomes comparable with an anisotropy value
International Nuclear Information System (INIS)
Takahashi, Y.
1986-01-01
A brief but systematic discussion of the Schrodinger field is presented from the view point of quantized field theory. It is pointed out that the local momentum conservation equation is not of the usual continuity equation type when two-body potential interaction is presented and nevertheless the total momentum is globally conserved. The Schrodinger equation can be cast into a multicomponent equation containing only first order derivatives, depending on its spin contents. In case of spin 1/2, the g-factor is shown to be 2 even in purely non-relativistic Schrodinger field, in contrast with the general belief that g=2 is a relativistic effect
International Nuclear Information System (INIS)
Vuillermot, P.A.
1988-01-01
We present and discuss three new theorems concerning the existence of smooth manifolds associated with certain infinite-dimensional dynamical systems defined from nonlinear Klein-Gordon equations of the form u tt (x, t) = u xx (x, t)-g(u(x, t)), where g: R → R is analytic and where (x, t) ε R 2 . In particular, we prove the nonexistence of small amplitude soliton bound state solutions in the classical Φ 4 -theory, a fact recently brought about by the perturbative analysis of Kruskal and Segur [fr
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...
Energy Technology Data Exchange (ETDEWEB)
Zuo, Da-Wei [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics; Shijiazhuang Tiedao University (China). Dept. of Mathematics and Physics; Gao, Yi-Tian; Sun, Yu-Hao; Feng, Yu-Jie; Xue, Long [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics
2014-10-15
The nonlinear Schroedinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration. Wave propagation and interaction are analyzed: (i) Bell-shape solitons, bright- and dark-rogue waves are found; (ii) the two-soliton interaction is elastic, i.e., the amplitude and velocity of each soliton remain unchanged after the interaction; (iii) the coefficient in the system affects the direction of the soliton propagation, patterns of the soliton interaction, distance, and direction of the first-order rogue-wave propagation, as well as the range and direction of the second-order rogue-wave interaction.
International Nuclear Information System (INIS)
Castro, J.J.B. de; Sudano, J.P.
1982-01-01
Explicit one-solition of a nonlinear Schrodinger equation with an inhomogeneous term are obtained by reducing the problem to the inverse-scattering method, extending the ideas of Zakhavov and Shabat. (Author) [pt
International Nuclear Information System (INIS)
Lyu, L.H.; Kan, J.R.
1989-01-01
Nonlinear one-dimensional constant-profile hydromagnetic wave solutions are obtained in finite-temperature two-fluid collisionless plasmas under adiabatic equation of state. The nonlinear wave solutions can be classified according to the wavelength. The long-wavelength solutions are circularly polarized incompressible oblique Alfven wave trains with wavelength greater than hudreds of ion inertial length. The oblique wave train solutions can explain the high degree of alignment between the local average magnetic field and the wave normal direction observed in the solar wind. The short-wavelength solutions include rarefaction fast solitons, compression slow solitons, Alfven solitons and rotational discontinuities, with wavelength of several tens of ion inertial length, provided that the upstream flow speed is less than the fast-mode speed
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
Liu, Yan; Guan, Yefeng; Li, Hai; Luo, Zhihuan; Mai, Zhijie
2017-08-01
We study families of stationary nonlinear localized modes and composite gray and anti-gray solitons in a one-dimensional linear waveguide array with dual phase-flip nonlinear point defects. Unstaggered fundamental and dipole bright modes are studied when the defect nonlinearity is self-focusing. For the fundamental modes, symmetric and asymmetric nonlinear modes are found. Their stable areas are studied using different defect coefficients and their total power. For the nonlinear dipole modes, the stability conditions of this type of mode are also identified by different defect coefficients and the total power. When the defect nonlinearity is replaced by the self-defocusing one, staggered fundamental and dipole bright modes are created. Finally, if we replace the linear waveguide with a full nonlinear waveguide, a new type of gray and anti-gray solitons, which are constructed by a kink and anti-kink pair, can be supported by such dual phase-flip defects. In contrast to the usual gray and anti-gray solitons formed by a single kink, their backgrounds on either side of the gray hole or bright hump have the same phase.
Quadratic spatial soliton interactions
Jankovic, Ladislav
Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30
Curilla, L.; Astrauskas, I.; Pugzlys, A.; Stajanca, P.; Pysz, D.; Uherek, F.; Baltuska, A.; Bugar, I.
2018-05-01
We demonstrate ultrafast soliton-based nonlinear balancing of dual-core asymmetry in highly nonlinear photonic crystal fiber at sub-nanojoule pulse energy level. The effect of fiber asymmetry was studied experimentally by selective excitation and monitoring of individual fiber cores at different wavelengths between 1500 nm and 1800 nm. Higher energy transfer rate to non-excited core was observed in the case of fast core excitation due to nonlinear asymmetry balancing of temporal solitons, which was confirmed by the dedicated numerical simulations based on the coupled generalized nonlinear Schrödinger equations. Moreover, the simulation results correspond qualitatively with the experimentally acquired dependences of the output dual-core extinction ratio on excitation energy and wavelength. In the case of 1800 nm fast core excitation, narrow band spectral intensity switching between the output channels was registered with contrast of 23 dB. The switching was achieved by the change of the excitation pulse energy in sub-nanojoule region. The performed detailed analysis of the nonlinear balancing of dual-core asymmetry in solitonic propagation regime opens new perspectives for the development of ultrafast nonlinear all-optical switching devices.
The Schrodinger Eigenvalue March
Tannous, C.; Langlois, J.
2011-01-01
A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…
Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong
2017-10-01
In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.
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.
International Nuclear Information System (INIS)
Ichikawa, Y.H.
1990-09-01
Plasma exhibits a full of variety of nonlinear phenomena. Active research in nonlinear plasma physics contributed to explore the concepts of soliton and chaos. Structure of soliton equations and dynamics of low dimensional Hamiltonian systems are discussed to emphasize the universality of these novel concepts in the wide branch of science and engineering. (author) 52 refs
Evolution of envelope solitons of ionization waves
International Nuclear Information System (INIS)
Ohe, K.; Hashimoto, M.
1985-01-01
The time evolution of a particle-like envelope soliton of ionization waves in plasma was investigated theoretically. The hydrodynamic equations of one spatial dimension were solved and the nonlinear dispersion relation was derived. For the amplitude of the wave the nonlinear Schroedinger equation was derived. Its soliton solution was interpreted as the envelope soliton which was experimentally found. The damping rate of the envelope soliton was estimated. (D.Gy.)
Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen
2018-01-01
In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.
Tunnelling effects of solitons in optical fibers with higher-order effects
Energy Technology Data Exchange (ETDEWEB)
Dai, Chao-Qing [Zhejiang A and F Univ., Lin' an (China). School of Sciences; Suzhou Univ., Jiangsu (China). School of Physical Science and Technology; Zhu, Hai-Ping [Zhejiang Lishui Univ., Zhejiang (China). School of Science; Zheng, Chun-Long [Shaoguan Univ., Guangdong (China). College of Physics and Electromechanical Engineering
2012-06-15
We construct four types of analytical soliton solutions for the higher-order nonlinear Schroedinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly. We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons. (orig.)
Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation
Kamvissis, Spyridon; Miller, Peter D
2003-01-01
This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing
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 evolution of astrophysical Alfven waves
Spangler, S. R.
1984-01-01
Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.
Exact bright and dark spatial soliton solutions in saturable nonlinear media
International Nuclear Information System (INIS)
Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.
2009-01-01
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.
Numerical computation of soliton dynamics for NLS equations in a driving potential
Directory of Open Access Journals (Sweden)
Marco Caliari
2010-06-01
Full Text Available We provide numerical computations for the soliton dynamics of the nonlinear Schrodinger equation with an external potential. After computing the ground state solution r of a related elliptic equation we show that, in the semi-classical regime, the center of mass of the solution with initial datum built upon r is driven by the solution to $ddot x=- abla V(x$. Finally, we provide examples and analyze the numerical errors in the two dimensional case when V is a harmonic potential.
International Nuclear Information System (INIS)
Su, Chuan-Qi; Gao, Yi-Tian; Yu, Xin; Xue, Long; Aviation Univ. of Air Force, Liaoning
2015-01-01
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.
Helmholtz bright and boundary solitons
Energy Technology Data Exchange (ETDEWEB)
Christian, J M [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P [Departmento de TeorIa de la Senal y Comunicaciones e IngenierIa Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)
2007-02-16
We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts.
Helmholtz bright and boundary solitons
International Nuclear Information System (INIS)
Christian, J M; McDonald, G S; Chamorro-Posada, P
2007-01-01
We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts
Motion of a magnetic soliton about a lattice soliton in a Heisenberg chain
International Nuclear Information System (INIS)
Nayyar, A.H.; Murtaza, G.
1981-08-01
As an example of interaction between two solitons belonging to different species, a semiclassical study of the nonlinear dynamics of a coupled magnon-phonon system in a one-dimensional Heisenberg ferromagnet is made, where both the lattice and the spin systems are taken with their respective nonlinear interactions. The lattice soliton is shown to introduce spatial inhomogeneities into the propagation of the magnetic soliton resulting in (a) the trapping of the magnetic soliton in the harmonic field of the lattice soliton and (b) the amplitude and the width of the magnetic soliton becoming time-dependent. (author)
Zhen, Hui-Ling; Tian, Bo; Xie, Xi-Yang; Wu, Xiao-Yu; Wen, Xiao-Yong
2018-02-01
On our previous construction [H. L. Zhen et al., Phys. Plasmas 23, 052301 (2016)] of the soliton solutions of a model describing the dynamics of the dust particles in a weakly ionized, collisional dusty plasma comprised of the negatively charged cold dust particles, hot ions, hot electrons, and stationary neutrals in the presence of an external static magnetic field, Ali et al. [Phys. Plasmas 24, 094701 (2017)] have commented that there exists a different form of Eq. (4) from that shown in Zhen et al. [Phys. Plasmas 23, 052301 (2016)] and that certain interesting phenomena with the dust neutral collision frequency ν0>0 are ignored in Zhen et al. [Phys. Plasmas 23, 052301 (2016)]. In this Reply, according to the transformation given by the Ali et al. [Phys. Plasmas 24, 094701 (2017)] comment, we present some one-, two-, and N-soliton solutions which have not been obtained in the Ali et al. [Phys. Plasmas 24, 094701 (2017)] comment. We point out that our previous solutions in Zhen et al. [Phys. Plasmas 23, 052301 (2016)] are still valid because of the similarity between the two dispersion relations of previous solutions in Zhen et al. [Phys. Plasmas 23, 052301 (2016)] and the solutions presented in this Reply. Based on our soliton solutions in this Reply, it is found that the soliton amplitude is inversely related to Zd and B0, but positively related to md and α, where α refers to the coefficient of the nonlinear term, Zd and md are the charge number and mass of a dust particle, respectively, B0 represents the strength of the external static magnetic field. We also find that the two solitons are always in parallel during the propagation.
Mann, Nishan; Hughes, Stephen
2018-02-01
We present the analytical and numerical details behind our recently published article [Phys. Rev. Lett. 118, 253901 (2017), 10.1103/PhysRevLett.118.253901], describing the impact of disorder-induced multiple scattering on counterpropagating solitons in photonic crystal waveguides. Unlike current nonlinear approaches using the coupled mode formalism, we account for the effects of intraunit cell multiple scattering. To solve the resulting system of coupled semilinear partial differential equations, we introduce a modified Crank-Nicolson-type norm-preserving implicit finite difference scheme inspired by the transfer matrix method. We provide estimates of the numerical dispersion characteristics of our scheme so that optimal step sizes can be chosen to either minimize numerical dispersion or to mimic the exact dispersion. We then show numerical results of a fundamental soliton propagating in the presence of multiple scattering to demonstrate that choosing a subunit cell spatial step size is critical in accurately capturing the effects of multiple scattering, and illustrate the stochastic nature of disorder by simulating soliton propagation in various instances of disordered photonic crystal waveguides. Our approach is easily extended to include a wide range of optical nonlinearities and is applicable to various photonic nanostructures where power propagation is bidirectional, either by choice, or as a result of multiple scattering.
Schrodinger cat state generation using a slow light
International Nuclear Information System (INIS)
Ham, B. S.; Kim, M. S.
2003-01-01
We show a practical application of giant Kerr nonlinearity to quantum information processing based on superposition of two distinct macroscopic states- Schrodinger cat state. The giant Kerr nonlinearity can be achieved by using electromagnetically induced transparency, in which light propagation should be slowed down so that a pi-phase shift can be easily obtained owing to increased interaction time.
Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar
2018-05-01
The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.
International Nuclear Information System (INIS)
Li Juan; Zhang Haiqiang; Xu Tao; Zhang, Ya-Xing; Tian Bo
2007-01-01
For the long-distance communication and manufacturing problems in optical fibers, the propagation of subpicosecond or femtosecond optical pulses can be governed by the variable-coefficient nonlinear Schroedinger equation with higher order effects, such as the third-order dispersion, self-steepening and self-frequency shift. In this paper, we firstly determine the general conditions for this equation to be integrable by employing the Painleve analysis. Based on the obtained 3 x 3 Lax pair, we construct the Darboux transformation for such a model under the corresponding constraints, and then derive the nth-iterated potential transformation formula by the iterative process of Darboux transformation. Through the one- and two-soliton-like solutions, we graphically discuss the features of femtosecond solitons in inhomogeneous optical fibers
International Nuclear Information System (INIS)
Omura, Yoshiharu; Matsumoto, Hiroshi.
1989-01-01
Past theoretical and numerical studies of the nonlinear evolution of electromagnetic cyclotron waves are reviewed. Such waves are commonly observed in space plasmas such as Alfven waves in the solar wind or VLF whistler mode waves in the magnetosphere. The use of an electromagnetic full-particle code to study an electron cyclotron wave and of an electromagnetic hybrid code to study an ion cyclotron wave is demonstrated. Recent achievements in the simulations of nonlinear revolution of electromagnetic cyclotron waves are discussed. The inverse cascading processes of finite-amplitude whistler and Alfven waves is interpreted in terms of physical elementary processes. 65 refs
Soliton Steering by Longitudinal Modulation of the Nonlinearity in Waveguide Arrays
Assanto, Gaetano; Cisneros, Luis A.; Minzoni, Antonmaria A.; Skuse, Benjamin D.; Smyth, Noel F.; Worthy, Annette L.
2010-01-01
We show how discrete solitary waves in one and two-dimensional waveguide arrays can be steered across the lattice via the introduction of a longitudinal periodic modulation of the nonlinear response. Through parametric energy transfer from the modulation to the solitary wave, the latter can increase its width and overcome the Peierls-Nabarro potential to propagate freely.
Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong
2017-07-01
The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.
International Nuclear Information System (INIS)
Scully, M O
2008-01-01
The time dependent Schrodinger equation is frequently 'derived' by postulating the energy E → i h-bar (∂/∂t) and momentum p-vector → ( h-bar /i)∇ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely 'a particle is what a particle detector detects.' This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation
Optical spatial solitons: historical overview and recent advances.
Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N
2012-08-01
Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a
Solitonic Dispersive Hydrodynamics: Theory and Observation
Maiden, Michelle D.; Anderson, Dalton V.; Franco, Nevil A.; El, Gennady A.; Hoefer, Mark A.
2018-04-01
Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.
Spatiotemporal optical solitons
International Nuclear Information System (INIS)
Malomed, Boris A; Mihalache, Dumitru; Wise, Frank; Torner, Lluis
2005-01-01
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)
Assessment of Schrodinger Eigenmaps for target detection
Dorado Munoz, Leidy P.; Messinger, David W.; Czaja, Wojtek
2014-06-01
Non-linear dimensionality reduction methods have been widely applied to hyperspectral imagery due to its structure as the information can be represented in a lower dimension without losing information, and because the non-linear methods preserve the local geometry of the data while the dimension is reduced. One of these methods is Laplacian Eigenmaps (LE), which assumes that the data lies on a low dimensional manifold embedded in a high dimensional space. LE builds a nearest neighbor graph, computes its Laplacian and performs the eigendecomposition of the Laplacian. These eigenfunctions constitute a basis for the lower dimensional space in which the geometry of the manifold is preserved. In addition to the reduction problem, LE has been widely used in tasks such as segmentation, clustering, and classification. In this regard, a new Schrodinger Eigenmaps (SE) method was developed and presented as a semi-supervised classification scheme in order to improve the classification performance and take advantage of the labeled data. SE is an algorithm built upon LE, where the former Laplacian operator is replaced by the Schrodinger operator. The Schrodinger operator includes a potential term V, that, taking advantage of the additional information such as labeled data, allows clustering of similar points. In this paper, we explore the idea of using SE in target detection. In this way, we present a framework where the potential term V is defined as a barrier potential: a diagonal matrix encoding the spatial position of the target, and the detection performance is evaluated by using different targets and different hyperspectral scenes.
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...
Dark Solitons in FPU Lattice Chain
Wang, Deng-Long; Yang, Ru-Shu; Yang, You-Tian
2007-11-01
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.
Dark Solitons in FPU Lattice Chain
International Nuclear Information System (INIS)
Wang Denglong; Yang Youtian; Yang Rushu
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.
International Nuclear Information System (INIS)
Fewo, S I; Kenfack-Jiotsa, A; Kofane, T C
2006-01-01
With the help of the one-dimensional quintic complex Ginzburg-Landau equation (CGLE) as perturbations of the nonlinear Schroedinger equation (NLSE), we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fibre optic links. The equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance, and also to analyse effects of initial amplitude and width on the propagating pulse. Nonlinear gain is shown to be beneficial in stabilizing DM solitons. A fully numerical simulation of the one-dimensional quintic CGLE as perturbations of NLSE finally tests the results of the CV theory. A good agreement is observed between both methods
Interaction of Langmuir solitons with sound
International Nuclear Information System (INIS)
Kurin, V.V.; Fraiman, G.M.
1981-01-01
The adiabatic approximation is used to study the interaction of Langmuir solitons with long ion-acoustic waves. The finite acoustic velocity gives rise to an effective mass for the soliton which is quite different from that in the approximation of a local nonlinearity. The force acting on a soliton, averaged over the period of the acoustic wave, is derived. The system of kinetic equations is analyzed in the approximation of random phases of the acoustic waves. The interaction of acoustic waves with solitons causes the acoustic spectrum to become more nearly isotropic, and the solitons are effectively damped
Novel energy sharing collisions of multicomponent solitons
Indian Academy of Sciences (India)
2015-10-21
Oct 21, 2015 ... Abstract. 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.
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties...... of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped...... narrow spikes. The influence of the point impurities on this dynamics is also investigated....
International Nuclear Information System (INIS)
Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying
2013-01-01
We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.
Numerical study of fractional nonlinear Schrodinger equations
Klein, Christian; Sparber, Christof; Markowich, Peter A.
2014-01-01
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass
International Nuclear Information System (INIS)
Liu Wenjun; Tian Bo; Xu Tao; Sun Kun; Jiang Yan
2010-01-01
Symbolically investigated in this paper is a nonlinear Schroedinger equation with the varying dispersion and nonlinearity for the propagation of optical pulses in the normal dispersion regime of inhomogeneous optical fibers. With the aid of the Hirota method, analytic one- and two-soliton solutions are obtained. Relevant properties of physical and optical interest are illustrated. Different from the previous results, both the bright and dark solitons are hereby derived in the normal dispersion regime of the inhomogeneous optical fibers. Moreover, different dispersion profiles of the dispersion-decreasing fibers can be used to realize the soliton control. Finally, soliton interaction is discussed with the soliton control confirmed to have no influence on the interaction. The results might be of certain value for the study of the signal generator and soliton control.
Deceleration of solitons in molecular chains
International Nuclear Information System (INIS)
Davydov, A.S.; Eremko, A.A.
1980-01-01
Effects of external actions on solitons arising under local excitations in molecular quasi-one-dimensional chains are investigated. The main formulas describing free solitons are presented. The motion of solitons in the presence of the force of friction proportional to their velocity is studied. It is shown that in this case the soliton velocity decreases with time in an exponential manner. It is shown that if the forces of friction are proportional to the square of velocity, the velocity decreases with time according to a linear law. The motion of solitons is investigated an the presence of small local non-uniformities or external fields. It is shown that an this case the soliton centre moves according to the Newton law in which however the force is determined by the integral expression. The conclusion is made that it is impossible to describe correctly the dynamic properties of solitons without taking into account physical factors causing the nonlinearity
Dynamical symmetries of semi-linear Schrodinger and diffusion equations
International Nuclear Information System (INIS)
Stoimenov, Stoimen; Henkel, Malte
2005-01-01
Conditional and Lie symmetries of semi-linear 1D Schrodinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrodinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf 3 ) C . We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf 3 ) C are classified and the complete list of conditionally invariant semi-linear Schrodinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed
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.
DEFF Research Database (Denmark)
Bache, Morten; Guo, Hairun; Zhou, Binbin
2013-01-01
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...... 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...
Multiple soliton production and the Korteweg-de Vries equation.
Hershkowitz, N.; Romesser, T.; Montgomery, D.
1972-01-01
Compressive square-wave pulses are launched in a double-plasma device. Their evolution is interpreted according to the Korteweg-de Vries description of Washimi and Taniuti. Square-wave pulses are an excitation for which an explicit solution of the Schrodinger equation permits an analytical prediction of the number and amplitude of emergent solitons. Bursts of energetic particles (pseudowaves) appear above excitation voltages greater than an electron thermal energy, and may be mistaken for solitons.
Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)
1995-01-01
This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.
Fractional Schrodinger equations with new conditions
Directory of Open Access Journals (Sweden)
Abderrazek Benhassine
2018-01-01
Full Text Available In this article, we study the nonlinear fractional Schrodinger equation $$\\displaylines{ (-\\Delta^{\\alpha}u+ V(xu= f(x,u\\cr u\\in H^{\\alpha}(\\mathbb{R}^{n},\\mathbb{R}, }$$ where $(-\\Delta^{\\alpha}(\\alpha \\in (0, 1$ stands for the fractional Laplacian of order $\\alpha$, $x\\in \\mathbb{R}^{n}$, $V\\in C(\\mathbb{R}^{n},\\mathbb{R}$ may change sign and f is only locally defined near the origin with respect to u. Under some new assumptions on V and f, we show that the above system has infinitely many solutions near the origin. Some examples are also given to illustrate our main theoretical result.
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.
Critical behavior from Schrodinger representation
International Nuclear Information System (INIS)
Suranyi, P.
1992-01-01
In this paper, the Schrodinger equation for φ 4 field theory is reduced to an infinite set of integral equations. A systematic truncation scheme is proposed and it is solved in second order to obtain the approximate critical behavior of the renormalized mass. The correlation exponent is given as a solution of a transcendental equation. It is in good agreement with the Ising model in all physical dimensions
Spectral tunneling of lattice nonlocal solitons
International Nuclear Information System (INIS)
Kartashov, Yaroslav V.; Torner, Lluis; Vysloukh, Victor A.
2010-01-01
We address spectral tunneling of walking spatial solitons in photorefractive media with nonlocal diffusion component of the nonlinear response and an imprinted shallow optical lattice. In contrast to materials with local nonlinearities, where solitons traveling across the lattice close to the Bragg angle suffer large radiative losses, in photorefractive media with diffusion nonlinearity resulting in self-bending, solitons survive when their propagation angle approaches and even exceeds the Bragg angle. In the spatial frequency domain this effect can be considered as tunneling through the band of spatial frequencies centered around the Bragg frequency where the spatial group velocity dispersion is positive.
Dissipative Solitons that Cannot be Trapped
International Nuclear Information System (INIS)
Pardo, Rosa; Perez-Garcia, Victor M.
2006-01-01
We show that dissipative solitons in systems with high-order nonlinear dissipation cannot survive in the presence of trapping potentials of the rigid wall or asymptotically increasing type. Solitons in such systems can survive in the presence of a weak potential but only with energies out of the interval of existence of linear quantum mechanical stationary states
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...
International Nuclear Information System (INIS)
Aichelburg, P.C.; Embacher, F.
1987-01-01
In previous work solitons of N = 2 supergravity were described as test particles in an external supergravity field. In the present paper we derive the effective interaction of two solitons by inserting a classical soliton configuration for the background into the Lagrangian and apply a slow-motion and large-distance approximation. We obtain the interaction potential to lowest order that incorporates the effect of the supercharge. The resulting classical system is quantized and, as a final step, an effective quantum field theory is formulated. (Author)
The dark soliton on a cnoidal wave background
International Nuclear Information System (INIS)
Shin, H J
2005-01-01
We find a solution of the dark soliton lying on a cnoidal wave background in a defocusing medium. We use the method of Darboux transformation, which is applied to the cnoidal wave solution of the defocusing nonlinear Schroedinger equation. Interesting characteristics of the dark soliton, i.e., the velocity and greyness, are calculated and compared with those of the dark soliton lying on a continuous wave background. We also calculate the shift of the crest of the cnoidal wave along the soliton
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
Generalized sine-Gordon solitons
International Nuclear Information System (INIS)
Santos, C dos; Rubiera-Garcia, D
2011-01-01
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)
International Nuclear Information System (INIS)
Brekke, L.; Imbo, T.D.
1992-01-01
The authors study the inequivalent quantizations of (1 + 1)-dimensional nonlinear sigma models with space manifold S 1 and target manifold X. If x is multiply connected, these models possess topological solitons. After providing a definition of spin and statistics for these solitons and demonstrating a spin-statistics correlation, we give various examples where the solitons can have exotic statistics. In some of these models, the solitons may obey a generalized version of fractional statistics called ambistatistics. In this paper the relevance of these 2d models to the statistics of vortices in (2 + 1)-dimensional spontaneously broken gauge theories is discussed. The authors close with a discussion concerning the extension of our results to higher dimensions
International Nuclear Information System (INIS)
Aichelburg, P.C.; Embacher, F.
1987-01-01
The motion of a soliton in a supergravity background configuration is studied. The dynamics of the soliton is desribed by a trajectory in curved N = 2 superspace. For the proposed Langrangian the moments, the constraints and the generators of local supertranslations are displayed. An additional local gauge symmetry is exhibited. Special emphasis is laid on the classical equations of motion. These turn out to be a supersymmetric generalization of Papapetrou's equation of motion for a spinning particle in a gravitational field. (Author)
International Nuclear Information System (INIS)
Friedberg, R.
1977-01-01
It is pointed out that the study of solitons offers a new departure for the problem of handling bound states in relativistic quantum field theory which has hampered development of a simple conventional model of hadrons. The principle is illustrated by the case of a quantum mechanical particle moving in two dimensions under the centrally symmetric and quasi-harmonic potential. Restriction is made to nontopological solitons. These ideas are applied to a model of hadrons. 10 references
DEFF Research Database (Denmark)
Zhou, Binbin; Guo, Hairun; Bache, Morten
2015-01-01
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 with...... 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....... 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...
Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser
Liu, Meng; Li, Heng; Luo, Ai-Ping; Cui, Hu; Xu, Wen-Cheng; Luo, Zhi-Chao
2018-03-01
Ultrafast fiber lasers have been demonstrated to be great platforms for the investigation of soliton dynamics. The soliton molecules, as one of the most fascinating nonlinear phenomena, have been a hot topic in the field of nonlinear optics in recent years. Herein, we experimentally observed the real-time evolving behavior of soliton molecule in an ultrafast fiber laser by using the dispersive Fourier transformation technology. Several types of evolving soliton molecules were obtained in our experiments, such as soliton molecules with monotonically or chaotically evolving phase, flipping and hopping phase. These results would be helpful to the communities interested in soliton nonlinear dynamics as well as ultrafast laser technologies.
de Silva, Nalin
2010-01-01
Schr\\"odinger's cat appears to have been harassed in a chamber during the past eighty years or so by interpreting the role of the observer as a person, who sets an experiment and then observes results, may be after some time. The realist position tells us that the physical processes would take place independent of the observer with well defined properties, whereas the positivist position wants us to believe that nothing can be said of a system when it is not being observed. In this paper we q...
Existence of solutions to quasilinear Schrodinger equations with indefinite potential
Directory of Open Access Journals (Sweden)
Zupei Shen
2015-04-01
Full Text Available In this article, we study the existence and multiplicity of solutions of the quasilinear Schrodinger equation $$ -u''+V(xu-(|u| ^2''u=f(u $$ on $\\mathbb{R}$, where the potential $V$ allows sign changing and the nonlinearity satisfies conditions weaker than the classical Ambrosetti-Rabinowitz condition. By a local linking theorem and the fountain theorem, we obtain the existence and multiplicity of solutions for the equation.
Solitons in plasma and other dispersive media
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Wadati, Miki.
1977-03-01
A review is given to recent development of extensive studies of nonlinear waves with purpose of showing methods of systematic analysis of nonlinear phenomena has been now established on the basis of new concept ''soliton''. Firstly, characteristic properties of various kinds of solitons are discussed with illustration of typical nonlinear evolution equations. Brief discussions are also given to basic mechanisms which ensure the remarkable stability and individuality of solitons. The reductive perturbation theory is a key method to reduce a given nonlinear system to a soliton system. Introductory survey is presented for an example of ionic mode in plasmas, although the method can be applied to any dispersive medium. Central subject of the present review is the analytical methods of solving nonlinear evolution equations. The inverse method, the Beacklund transformation and the conservation laws are discussed to emphasize that very firm analytical basis is now available to disentangle the nonlinear problems. Finally, a notion of ''dressed'' solitons is introduced on basis of the higher order analysis of the reductive perturbation theory. In spite of the fact that success is restricted so far only for the one dimensional system, the achievement of soliton physics encourages us to face dawn of nonlinear physics with a confident expectation for forthcoming break through in the field. (auth.)
Intermode Breather Solitons in Optical Microresonators
Guo, Hairun; Lucas, Erwan; Pfeiffer, Martin H. P.; Karpov, Maxim; Anderson, Miles; Liu, Junqiu; Geiselmann, Michael; Jost, John D.; Kippenberg, Tobias J.
2017-10-01
Dissipative solitons can be found in a variety of systems resulting from the double balance between dispersion and nonlinearity, as well as gain and loss. Recently, they have been observed to spontaneously form in Kerr nonlinear microresonators driven by a continuous wave laser, providing a compact source of coherent optical frequency combs. As optical microresonators are commonly multimode, intermode interactions, which give rise to avoided mode crossings, frequently occur and can alter the soliton properties. Recent works have shown that avoided mode crossings cause the soliton to acquire a single-mode dispersive wave, a recoil in the spectrum, or lead to soliton decay. Here, we show that avoided mode crossings can also trigger the formation of breather solitons, solitons that undergo a periodic evolution in their amplitude and duration. This new breather soliton, referred to as an intermode breather soliton, occurs within a laser detuning range where conventionally stationary (i.e., stable) dissipative Kerr solitons are expected. We experimentally demonstrate the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators) and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We show that the breathing is associated with a periodic energy exchange between the soliton and a second optical mode family, a behavior that can be modeled by a response function acting on dissipative solitons described by the Lugiato-Lefever model. The observation of breathing dynamics in the conventionally stable soliton regime is relevant to applications in metrology such as low-noise microwave generation, frequency synthesis, or spectroscopy.
Stable rotating dipole solitons in nonlocal media
DEFF Research Database (Denmark)
Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.
2006-01-01
We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons.......We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons....
Bright, dark and singular optical solitons in a cascaded system
International Nuclear Information System (INIS)
Zhou, Qin; Zhu, Qiuping; Yu, Hua; Liu, Yaxian; Wei, Chun; Yao, Ping; Bhrawy, Ali H; Biswas, Anjan
2015-01-01
This work studies nonlinear dynamics of optical solitons in a cascaded system with Kerr law nonlinearity and spatio-temporal dispersion. The mathematical model that describes the propagation of optical solitons through a cascaded system is given by the vector-coupled nonlinear Schrödinger equation. It is investigated analytically using three integration algorithms. The Jacobian elliptic equation expansion method, Bernoulli equation expansion approach and Riccati equation expansion scheme are the integration tools of this model that are recruited to extract singular, bright and dark solitons. The restrictions that need to hold for the existence of these solitons are derived. (paper)
Helmholtz solitons in power-law optical materials
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.
2007-01-01
A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified
International Nuclear Information System (INIS)
Tang, D.Y.; Zhao, L.M.; Zhao, B.; Liu, A.Q.
2005-01-01
We report results of numerical simulations on multiple-soliton generation and soliton energy quantization in a soliton fiber ring laser passively mode locked by using the nonlinear polarization rotation technique. We found numerically that the formation of multiple solitons in the laser is caused by a peak-power-limiting effect of the laser cavity. It is also the same effect that suppresses the soliton pulse collapse, an intrinsic feature of solitons propagating in gain media, and makes the solitons stable in the laser. Furthermore, we show that the soliton energy quantization observed in the lasers is a natural consequence of the gain competition between the multiple solitons. Enlightened by the numerical result we speculate that multisoliton formation and soliton energy quantization observed in other types of soliton fiber lasers could have a similar mechanism
Schrodinger representation in renormalizable quantum field theory
International Nuclear Information System (INIS)
Symanzik, K.
1983-01-01
The problem of the Schrodinger representation arose from work on the Nambu-Goto Ansatz for integration over surfaces. Going beyond semiclassical approximation leads to two problems of nonrenormalizibility and of whether Dirichlet boundary conditions can be imposed on a ''Euclidean'' quantum field theory. The Schrodinger representation is constructed in a way where the principles of general renormalization theory can be refered to. The Schrodinger function of surface terms is studied, as well as behaviour at the boundary. The Schrodinger equation is derived. Completeness, unitarity, and computation of expectation values are considered. Extensions of these methods into other Bose field theories such as Fermi fields and Marjorana fields is straightforward
Vector pulsing soliton of self-induced transparency in waveguide
International Nuclear Information System (INIS)
Adamashvili, G.T.
2015-01-01
A theory of an optical resonance vector pulsing soliton in waveguide is developed. A thin transition layer containing semiconductor quantum dots forms the boundary between the waveguide and one of the connected media. Analytical and numerical solutions for the optical vector pulsing soliton in waveguide are obtained. The vector pulsing soliton in the presence of excitonic and bi-excitonic excitations is compared with the soliton for waveguide TM-modes with parameters that can be used in modern optical experiments. It is shown that these nonlinear waves have significantly different parameters and shapes. - Highlights: • An optical vector pulsing soliton in a planar waveguide is presented. • Explicit form of the optical vector pulsing soliton are obtained. • The vector pulsing soliton and the soliton have different parameters and profiles
High-dimensional chaos from self-sustained collisions of solitons
Energy Technology Data Exchange (ETDEWEB)
Yildirim, O. Ozgur, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Cavium, Inc., 600 Nickerson Rd., Marlborough, Massachusetts 01752 (United States); Ham, Donhee, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Harvard University, 33 Oxford St., Cambridge, Massachusetts 02138 (United States)
2014-06-16
We experimentally demonstrate chaos generation based on collisions of electrical solitons on a nonlinear transmission line. The nonlinear line creates solitons, and an amplifier connected to it provides gain to these solitons for their self-excitation and self-sustenance. Critically, the amplifier also provides a mechanism to enable and intensify collisions among solitons. These collisional interactions are of intrinsically nonlinear nature, modulating the phase and amplitude of solitons, thus causing chaos. This chaos generated by the exploitation of the nonlinear wave phenomena is inherently high-dimensional, which we also demonstrate.
International Nuclear Information System (INIS)
Olsen, M.; Smith, H.; Scott, A.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 is intended for lecture demonstrations. 19 references, 6 figures
Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium
Dasanayaka, Sahan; Atai, Javid
2011-08-01
Interactions between quiescent solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are systematically investigated. In a previous work two disjoint families of solitons were identified in this model. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity (Type 1). On the other hand, the quintic nonlinearity is dominant in the other family (Type 2). For weak to moderate dispersive reflectivity, two in-phase solitons will attract and collide. Possible collision outcomes include merger to form a quiescent soliton, formation of three solitons including a quiescent one, separation after passing through each other once, asymmetric separation after several quasielastic collisions, and soliton destruction. Type 2 solitons are always destroyed by collisions. Solitons develop sidelobes when dispersive reflectivity is strong. In this case, it is found that the outcome of the interactions is strongly dependent on the initial separation of solitons. Solitons with sidelobes will collide only if they are in-phase and their initial separation is below a certain critical value. For larger separations, both in-phase and π-out-of-phase Type 1 and Type 2 solitons may either repel each other or form a temporary bound state that subsequently splits into two separating solitons. Additionally, in the case of Type 2 solitons, for certain initial separations, the bound state disintegrates into a single moving soliton.
Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.
2018-04-01
The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.
Soliton interaction in quadratic and cubic bulk media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole
2000-01-01
Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... 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...
Black and gray Helmholtz-Kerr soliton refraction
International Nuclear Information System (INIS)
Sanchez-Curto, Julio; Chamorro-Posada, Pedro; McDonald, Graham S.
2011-01-01
Refraction of black and gray solitons at boundaries separating different defocusing Kerr media is analyzed within a Helmholtz framework. A universal nonlinear Snell's law is derived that describes gray soliton refraction, in addition to capturing the behavior of bright and black Kerr solitons at interfaces. Key regimes, defined by beam and interface characteristics, are identified, and predictions are verified by full numerical simulations. The existence of a unique total nonrefraction angle for gray solitons is reported; both internal and external refraction at a single interface is shown possible (dependent only on incidence angle). This, in turn, leads to the proposal of positive or negative lensing operations on soliton arrays at planar boundaries.
Uniform decay for a local dissipative Klein-Gordon-Schrodinger type system
Directory of Open Access Journals (Sweden)
Marilena N. Poulou
2012-10-01
Full Text Available In this article, we consider a nonlinear Klein-Gordon-Schrodinger type system in $mathbb{R}^n$, where the nonlinear term exists and the damping term is effective. We prove the existence and uniqueness of a global solution and its exponential decay. The result is achieved by using the multiplier technique.
Directory of Open Access Journals (Sweden)
Kai Tsuruta
2013-05-01
Full Text Available We prove the existence of the wave operator for the Klein-Gordon-Schrodinger system with Yukawa coupling. This non-linearity type is below Strichartz scaling, and therefore classic perturbation methods will fail in any Strichartz space. Instead, we follow the "first iteration method" to handle these critical non-linearities.
Quantum Computer Games: Schrodinger Cat and Hounds
Gordon, Michal; Gordon, Goren
2012-01-01
The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…
Comparison of the Schrodinger and Salpeter equations
International Nuclear Information System (INIS)
Jacobs, S.; Olsson, M.G.
1985-01-01
A unified approach to the solution of the Schrodinger and spinless Salpeter equations is presented. Fits to heavy quark bound state energies using various potential models are employed to determine whether the Salpeter equation provides a better description of heavy quark systems than the Schrodinger equation
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.
International Nuclear Information System (INIS)
Aichelburg, P.C.; Embacher, F.
1987-01-01
The Langrangian for a single free soliton in N = 2 supergravity as proposed in an earlier paper, is studied. We analyze the algebra of constraints and discuss the local gauge symmetry due to the existence of first class constraints. The classical motion as well as a Gupta-Bleuler type quantization are given. (Author)
Soliton robustness in optical fibers
International Nuclear Information System (INIS)
Menyuk, C.R.
1993-01-01
Simulations and experiments indicate that solitons in optical fibers are robust in the presence of Hamiltonian deformations such as higher-order dispersion and birefringence but are destroyed in the presence of non-Hamiltonian deformations such as attenuation and the Raman effect. Two hypotheses are introduced that generalize these observations and give a recipe for when deformations will be Hamiltonian. Concepts from nonlinear dynamics are used to make these two hypotheses plausible. Soliton stabilization with frequency filtering is also briefly discussed from this point of view
International Nuclear Information System (INIS)
Walliser, Hans
2000-01-01
Chiral Lagrangians as effective field theories of QCD are successfully applied to meson physics in the framework of chiral perturbation theory. Because of their nonlinear structure these Lagrangians allow for static soliton solutions interpreted as baryons. Their semiclassical quantization, which provides the leading order in an 1/N C expansion with N C the number of colors, turned out to be insufficient to obtain satisfactory agreement with empirical baryon observables. However with N C =3, large corrections are expected in the next-to-leading order carried by mesonic fluctuations around the soliton background, which require renormalization to 1-loop. In contrast to chiral perturbation theory, the low-energy Lagrangian proves inapt and terms with an arbitrary number of gradients may in principle contribute. Assumptions about the a priori unknown higher chiral orders are tested by the scale-dependence of the results. For example, in the simple Sine-Gordon model with 1 scalar field in 1+1 dimensions, knowledge of the low-energy behavior together with the mere existence of an underlying 1-loop renormalizable scale-independent solitonic theory is sufficient to regain the full solution. Baryonic observables calculated within that framework generally lead to better agreement with experiment except for the axial quantities. For these quantities the 1/N C expansion does not converge sufficiently fast because the current algebra mixes different N C orders
Soliton concepts and protein structure
Krokhotin, Andrei; Niemi, Antti J.; Peng, Xubiao
2012-03-01
Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion from a relatively small number of components. Here we propose that the modular building blocks are made of the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. We find that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop-specific parameters, and we compute their statistical distribution in the Protein Data Bank (PDB). We explicitly construct a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop. The ensuing profiles cover practically all those proteins in PDB that have a resolution which is better than 2.0 Å, with a precision such that the average root-mean-square distance between the loop and its soliton is less than the experimental B-factor fluctuation distance. We also present two examples that describe how the loop library can be employed both to model and to analyze folded proteins.
Lattice solitons in Bose-Einstein condensates
International Nuclear Information System (INIS)
Efremidis, Nikolaos K.; Christodoulides, Demetrios N.
2003-01-01
We systematically study the properties of lattice solitons in Bose-Einstein condensates with either attractive or repulsive atom interactions. This is done, by exactly solving the mean-field Gross-Pitaevskii equation in the presence of a periodic potential. We find new families of lattice soliton solutions that are characterized by the position of the energy eigenvalue within the associated band structure. These include lattice solitons in condensates with either attractive or repulsive atom interactions that exist in finite or semi-infinite gaps, as well as nonlinear modes that exhibit atomic population cutoffs
Laser generated soliton waveguides in photorefractive crystals
International Nuclear Information System (INIS)
Vlad, V.I.; Fazio, E.; Bertolotti, M.; Bosco, A.; Petris, A.
2005-01-01
Non-linear photo-excited processes using the photorefractive effect are revisited with emphasis on spatial soliton generation in special laser beam propagation conditions. The soliton beams can create reversible or irreversible single-mode waveguides in the propagating materials. The important features are the 3D orientation and graded index profile matched to the laser fundamental mode. Bright spatial solitons are theoretically demonstrated and experimentally observed for the propagation of c.w. and pulsed femtosecond laser beams in photorefractive materials such as Bi 12 SiO 20 (BSO) and lithium niobate crystals. Applications in high coupling efficiency, adaptive optical interconnections and photonic crystal production are possible
Phase-locked Josephson soliton oscillators
DEFF Research Database (Denmark)
Holst, T.; Hansen, Jørn Bindslev; Grønbech-Jensen, N.
1991-01-01
Detailed experimental characterization of the phase-locking at both DC and at microwave frequencies is presented for two closely spaced Josephson soliton (fluxon) oscillators. In the phase-locked state, the radiated microwave power exhibited an effective gain. With one common bias source......, a frequency tunability of the phase-locked oscillators up to 7% at 10 GHz was observed. The interacting soliton oscillators were modeled by two inductively coupled nonlinear transmission lines...
Finite element method for time-space-fractional Schrodinger equation
Directory of Open Access Journals (Sweden)
Xiaogang Zhu
2017-07-01
Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.
Schr\\"odinger group and quantum finance
Romero, Juan M.; Lavana, Ulises; Martínez, Elio
2013-01-01
Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schr\\"odinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equation symmetries, the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schr\\"odinger algebra representation is co...
Transport by negative eddy viscosity in soliton turbulence
Tchen, C. M.
1986-01-01
The forced Schrodinger equation is used to describe the microhydrodynamical state of strong soliton turbulence. The Schrodinger equation is transformed into a master equation and is decomposed into a macrogroup, a microgroup, and a submicrogroup, representative of the three transport processes of spectral evolution, transport property, and relaxation. The kinetic equation for the macrodistribution is derived and reverted to the continuum by the method of moments in order to find the equation of spectral evolution. The spectral flow is found to be governed by three types of transport, which are discussed.
Directory of Open Access Journals (Sweden)
Chen Yue
Full Text Available The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated. Keywords: Quintic derivative NLS equation, Solitary wave solutions, Mathematical physics methods, 2000 MR Subject Classification: 35G20, 35Q53, 37K10, 49S05, 76A60
A Statistical Model for Soliton Particle Interaction in Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans; Truelsen, J.
1986-01-01
A statistical model for soliton-particle interaction is presented. A master equation is derived for the time evolution of the particle velocity distribution as induced by resonant interaction with Korteweg-de Vries solitons. The detailed energy balance during the interaction subsequently determines...... the evolution of the soliton amplitude distribution. The analysis applies equally well for weakly nonlinear plasma waves in a strongly magnetized waveguide, or for ion acoustic waves propagating in one-dimensional systems....
International Nuclear Information System (INIS)
Wilets, L.
1988-01-01
Soliton models are well-suited for dynamical calculations, such as hadron-hadron interactions and collisions, since for each variable in the Lagrangian the time derivative of that variable also appears. For such models, constrained (deformed) mean field solutions provide a basis for generator coordinate dynamical calculations. This requires the solution of a large number of coupled, nonlinear, differential equations involving the quark and scalar fields. The Henyey-Wilets method reduces the problem to the solution of a set of coupled, linear, inhomogeneous, differential equations to be iterated. In the chromodielectric model, color confinement is effected by the self and mutual interactios of the quarks through the chromelectric field. This requires the self-consistent calculation of the gluon propagator in a spatially varying dielectric function. This now involves the solution of a set of coupled, nonlinear integro-differential equations, which can be linearized and solved by iterations. The problem is computation intensive. 20 refs
Break up of bound-N-spatial-soliton in a ramp waveguide
Suryanto, A.; van Groesen, Embrecht W.C.
2002-01-01
We present an analytical and numerical investigation of the propagation of spatial solitons in a nonlinear waveguide with ramp linear refractive index profile (ramp waveguide). For the propagation of a single soliton beam in a ramp waveguide, the particle theory shows that the soliton beam follows a
The dynamics of short envelope solitons in media with controlled dispersion
International Nuclear Information System (INIS)
Aseeva, N.V.; Gromov, E.M.; Tyutin, V.V.
2007-01-01
The dynamics of short envelope solitons in media with controlled dispersion is investigated in the framework of the third-order nonlinear Schroedinger equation. Evolution of the solitons amplitude is analyzed in the adiabatic approximation. The existence of short envelope solitons independent from linear dispersion inhomogeneity is shown
Weyl solitons in three-dimensional optical lattices
Shang, Ce; Zheng, Yuanlin; Malomed, Boris A.
2018-04-01
Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.
Dynamical Instability and Soliton Concept
International Nuclear Information System (INIS)
Kartavenko, V.G.
1994-01-01
The problem of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is noted that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Rayleigh-Taylor type) instability, with the dispersion terms in the evolution equations. The spinodal instability and the Rayleigh-Taylor instability may compensate each other and lead to stable quasi-soliton type objects. The simple analytical model is presented to illustrate this physical picture. The time evolution of an initially compressed cold nuclear system is analysed in the framework of the inverse mean-field method. It is demonstrated that the nonlinearity and dispersion terms of the evolution equations can lead to clusterization in the final channel. 8 p
2013-01-01
In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of non-linear and dispersive effects in the medium. In this book, the authors discuss the interactions and theoretical and experimental challenges of solitons. Topics include soliton motion of electrons and its physical properties in coupled electron-phonon systems and ionic crystals; soliton excitations and its experimental evidence in molecular crystals; shapes and dynamics of semi-discrete solitons in arrayed and stacked waveguiding systems; ion-acoustic super solitons in plasma; diamond-controlled solitons and turbulence in extracellular matrix and lymphatic dynamics; and non-linear waves in strongly interacting relativistic fluids.
Escape angles in bulk chi((2)) soliton interactions
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole; Sørensen, Mads Peter
2002-01-01
We develop a theory for nonplanar interaction between two identical type I spatial solitons propagating at opposite, but arbitrary transverse angles in quadratic nonlinear (or so-called chi((2))) bulk, media. We predict quantitatively the outwards escape angle, below which the solitons turn around...
Matter-wave bright solitons in effective bichromatic lattice potentials
Indian Academy of Sciences (India)
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 ...
Dark and bright vortex solitons in electromagnetically induced transparent media
International Nuclear Information System (INIS)
Wu Xuan; Xie Xiaotao; Yang Xiaoxue
2006-01-01
We show that dark and bright vortex solitons can exist in three-state electromagnetically induced transparent media under some appropriate conditions. We also analyse the stability of the dark and bright vortex solitons. This work may provide other research opportunities in nonlinear optical experiments and may result in a substantial impact on technology
Soliton collapse during ionospheric heating
International Nuclear Information System (INIS)
Sheerin, J.P.; Nicholson, D.R.; Payne, G.L.; Duncan, L.M.
1984-01-01
We present analytical and numerical work which indicates that during ionospheric heating with high-powered hf radio waves, the oscillating two-stream instability may dominate the parametric decay instability. The oscillating two-stream instability saturates nonlinearly through the formation of solitons which undergo a collisionally damped collapse. Using the heater and radar facilities at Arecibo Observatory, we have investigated this phenomenon experimentally. Recent results from our theoretical and experimental investigations are presented
Supersymmetric extensions of Schrodinger-invariance
International Nuclear Information System (INIS)
Henkel, Malte; Unterberger, Jeremie
2006-01-01
The set of dynamic symmetries of the scalar free Schrodinger equation in d space dimensions gives a realization of the Schrodinger algebra that may be extended into a representation of the conformal algebra in d+2 dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-12 Levy-Leblond equation. An N=2 supersymmetric extension of these equations leads, respectively, to a 'super-Schrodinger' model and to the (3 vertical bar 2)-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras osp(2 vertical bar 2)-bar sh(2 vertical bar 2) and osp(2 vertical bar 4), respectively. The Schrodinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schrodinger-Neveu-Schwarz algebra sns (N) with N supercharges. Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of osp(2 vertical bar 4). If one includes both N=2 supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values
Analytic smoothing effect for the cubic hyperbolic Schrodinger equation in two space dimensions
Directory of Open Access Journals (Sweden)
Gaku Hoshino
2016-01-01
Full Text Available We study the Cauchy problem for the cubic hyperbolic Schrodinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.
Introduction to solitons and their applications in physics and biology
International Nuclear Information System (INIS)
Peyrard, M.
1995-01-01
The response of most of the physical systems to combined excitations is not a simple superposition of their response to individual stimuli. This is particularly true for biological systems in which the nonlinear effects are often the dominant ones. The intrinsic treatment of nonlinearities in mathematical models and physical systems has led to the emergence of the chaos and solitons concepts. The concept of soliton, relevant for systems with many degrees of freedom, provides a new tool in the studies of biomolecules because it has no equivalent in the world of linear excitations. The aim of this lecture is to present the main ideas that underline the soliton concept and to discuss some applications. Solitons are solitary waves, that propagate at constant speed without changing their shape. They are extremely stable to perturbations, in particular to collisions with small amplitude linear waves and with other solitons. Conditions to have solitons and equations of solitons propagation are analysed. Solitons can be divided into two main classes: topological and non-topological solitons which can be found at all scales and in various domains of physics and chemistry. Using simple examples, this paper shows how linear expansions can miss completely essential physical properties of a system. This is particularly characteristic for the pendulum chain example. Soliton theory offers alternative methods. Multiple scale approximations, or expansion on a soliton basis, can be very useful to provide a description of some physical phenomena. Nonlinear energy localization is also a very important concept valid for a large variety of systems. These concepts are probably even more relevant for biological molecules than for solid state physics, because these molecules are very deformable objects where large amplitude nonlinear motions or conformational changes are crucial for function. (J.S.). 14 refs., 9 figs
Coexistence of collapse and stable spatiotemporal solitons in multimode fibers
Shtyrina, Olga V.; Fedoruk, Mikhail P.; Kivshar, Yuri S.; Turitsyn, Sergei K.
2018-01-01
We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization.
Spectral long-range interaction of temporal incoherent solitons.
Xu, Gang; Garnier, Josselin; Picozzi, Antonio
2014-02-01
We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.
Understanding Soliton Spectral Tunneling as a Spectral Coupling Effect
DEFF Research Database (Denmark)
Guo, Hairun; Wang, Shaofei; Zeng, Xianglong
2013-01-01
Soliton eigenstate is found corresponding to a dispersive phase profile under which the soliton phase changes induced by the dispersion and nonlinearity are instantaneously counterbalanced. Much like a waveguide coupler relying on a spatial refractive index profile that supports mode coupling...... between channels, here we suggest that the soliton spectral tunneling effect can be understood supported by a spectral phase coupler. The dispersive wave number in the spectral domain must have a coupler-like symmetric profile for soliton spectral tunneling to occur. We show that such a spectral coupler...
Energy Technology Data Exchange (ETDEWEB)
Saleh, Mohammed F.; Biancalana, Fabio [Max Planck Institute for the Science of Light, Guenther-Scharowsky Str. 1, DE-91058 Erlangen (Germany)
2011-12-15
We present the details of our previously formulated model [Saleh et al., Phys. Rev. Lett. 107, 203902 (2011)] that governs pulse propagation in hollow-core photonic crystal fibers filled by an ionizable gas. By using perturbative methods, we find that the photoionization process induces the opposite phenomenon of the well-known Raman self-frequency redshift of solitons in solid-core glass fibers, as was recently experimentally demonstrated [Hoelzer et al., Phys. Rev. Lett. 107, 203901 (2011)]. This process is only limited by ionization losses, and leads to a constant acceleration of solitons in the time domain with a continuous blueshift in the frequency domain. By applying the Gagnon-Belanger gauge transformation, multipeak ''inverted gravitylike'' solitary waves are predicted. We also demonstrate that the pulse dynamics shows the ejection of solitons during propagation in such fibers, analogous to what happens in conventional solid-core fibers. Moreover, unconventional long-range nonlocal interactions between temporally distant solitons, unique of gas plasma systems, are predicted and studied. Finally, the effects of higher-order dispersion coefficients and the shock operator on the pulse dynamics are investigated, showing that the conversion efficiency of resonant radiation into the deep UV can be improved via plasma formation.
International Nuclear Information System (INIS)
Gopakumar, R.
2002-01-01
Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect
Energy Technology Data Exchange (ETDEWEB)
Gopakumar, R [Harish-Chandra Research Institute, Jhusi, Allahabad (India)
2002-05-15
Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect.
Joseph, Rose; Goorjian, Peter; Taflove, Allen
1993-01-01
Experimentalists have produced all-optical switches capable of 100-fs responses. To adequately model such switches, nonlinear effects in optical materials (both instantaneous and dispersive) must be included. In principle, the behavior of electromagnetic fields in nonlinear dielectrics can be determined by solving Maxwell's equations subject to the assumption that the electric polarization has a nonlinear relation to the electric field. However, until our previous work, the resulting nonlinear Maxwell's equations have not been solved directly. Rather, approximations have been made that result in a class of generalized nonlinear Schrodinger equations (GNLSE) that solve only for the envelope of the optical pulses. In this paper, we present first-time calculations from the vector nonlinear Maxwell's equations of femtosecond soliton propagation and scattering, including carrier waves, in two-dimensional systems of dielectric waveguides exhibiting the Kerr and Raman quantum effects. We use the finite-difference time-domain (FD-TD) method in an extension of our 1-D work. There, in a fundamental innovation, we treated the linear and nonlinear convolutions for the electric polarization as new dependent variables. By differentiating these convolutions in the time domain, we derived an equivalent system of coupled, nonlinear second-order ODE's. These equations together with Maxwell's equations form the system that is solved to determine the electromagnetic fields in inhomogeneous nonlinear dispersive media. Backstorage in time is limited to only that needed by the time-integration algorithm for the ODE's, rather than that needed to store the time-history of the kernel functions of the convolutions (1000-10,000 time steps). Thus, a 2-D nonlinear optics model from Maxwell's equations is now feasible.
Topological and non-topological soliton solutions to some time
Indian Academy of Sciences (India)
Topological and non-topological soliton solutions to some time-fractional differential equations ... These equations have been widely applied in many branches of nonlinear ... Department of Engineering Sciences, Faculty of Technology and ...
Accurate nonlocal theory for cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey
2007-01-01
We study soliton compression in bulk 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....
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...
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Author Affiliations. Lin Xiao-Gang1 Liu Wen-Jun2 Lei Ming2. Key Laboratory of Optoelectronic Technology & Systems (Chongqing University), Ministry of Education, Chongqing, China; School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876, China ...
New types of exact solutions for a breaking soliton equation
International Nuclear Information System (INIS)
Mei Jianqin; Zhang Hongqing
2004-01-01
In this paper based on a system of Riccati equations, we present a newly generally projective Riccati equation expansion method and its algorithm, which can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics. A typical breaking soliton equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain soliton-like solutions and periodic solutions. This algorithm can also be applied to other nonlinear differential equations
Intensity limits for stationary and interacting multi-soliton complexes
International Nuclear Information System (INIS)
Sukhorukov, Andrey A.; Akhmediev, Nail N.
2002-01-01
We obtain an accurate estimate for the peak intensities of multi-soliton complexes for a Kerr-type nonlinearity in the (1+1) dimension problem. Using exact analytical solutions of the integrable set of nonlinear Schroedinger equations, we establish a rigorous relationship between the eigenvalues of incoherently-coupled fundamental solitons and the range of admissible intensities. A clear geometrical interpretation of this effect is given
Large amplitude collective nuclear motion and soliton concept
International Nuclear Information System (INIS)
Kartavenko, V.G.; Joint Inst. for Nuclear Research, Dubna
1993-01-01
An application of a soliton theory methods to some nonlinear problems in low and intermediate energies (E ∼ 10--100MeV/nucleon) nucleus - nucleus collisions are presented. Linear and nonlinear excitations of the nuclear density are investigated in the framework of nuclear hydrodynamics. The problem of dynamical instability and clusterization phenomena in a breakup of excited nuclear systems are considered from the points of view of a soliton concept
Bistable Helmholtz solitons in cubic-quintic materials
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2007-01-01
We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations
Condensate bright solitons under transverse confinement
International Nuclear Information System (INIS)
Salasnich, L.; Reatto, L.; Parola, A.
2002-01-01
We investigate the dynamics of Bose-Einstein condensate bright solitons made of alkali-metal atoms with negative scattering length and under harmonic confinement in the transverse direction. Contrary to the one-dimensional (1D) case, the 3D bright soliton exists only below a critical attractive interaction that depends on the extent of confinement. Such a behavior is also found in multisoliton condensates with box boundary conditions. We obtain numerical and analytical estimates of the critical strength beyond which the solitons do not exist. By using an effective 1D nonpolynomial nonlinear Schroedinger equation, which accurately takes into account the transverse dynamics of cigarlike condensates, we numerically simulate the dynamics of the 'soliton train' reported in a recent experiment [Nature (London) 417, 150 (2002)]. Then, analyzing the macroscopic quantum tunneling of the bright soliton on a Gaussian barrier, we find that its interference in the tunneling region is strongly suppressed with respect to nonsolitonic case; moreover, the tunneling through a barrier breaks the shape invariance of the matter wave. Finally, we show that the collapse of the soliton is induced by the scattering on the barrier or by the collision with another matter wave when the density reaches a critical value, for which we derive an accurate analytical formula
Vibron Solitons and Soliton-Induced Infrared Spectra of Crystalline Acetanilide
Takeno, S.
1986-01-01
Red-shifted infrared spectra at low temperatures of amide I (C=O stretching) vibrations of crystalline acetanilide measured by Careri et al. are shown to be due to vibron solitons, which are nonlinearity-induced localized modes of vibrons arising from their nonlinear interactions with optic-type phonons. A nonlinear eigenvalue equation giving the eigenfrequency of stationary solitons is solved approximately by introducing lattice Green's functions, and the obtained result is in good agreement with the experimental result. Inclusion of interactions with acoustic phonons yields the Debye-Waller factor in the zero-phonon line spectrum of vibron solitons, in a manner analogous to the case of impurity-induced localized harmonic phonon modes in alkali halides.
New solitons connected to the Dirac equation
International Nuclear Information System (INIS)
Grosse, H.
1984-01-01
Imposing isospectral invariance for the one dimensional Dirac operator leads to systems of nonlinear partial differential equations. By constructing reflectionless potentials of the Dirac equation we obtain a new type of solitons for a system of modified Korteweg-de Vries equations. (Author)
Observation of soliton compression in silicon photonic crystals
Blanco-Redondo, A.; Husko, C.; Eades, D.; Zhang, Y.; Li, J.; Krauss, T.F.; Eggleton, B.J.
2014-01-01
Solitons are nonlinear waves present in diverse physical systems including plasmas, water surfaces and optics. In silicon, the presence of two photon absorption and accompanying free carriers strongly perturb the canonical dynamics of optical solitons. Here we report the first experimental demonstration of soliton-effect pulse compression of picosecond pulses in silicon, despite two photon absorption and free carriers. Here we achieve compression of 3.7 ps pulses to 1.6 ps with photonic crystal waveguide and an ultra-sensitive frequency-resolved electrical gating technique to detect the ultralow energies in the nanostructured device. Strong agreement with a nonlinear Schrödinger model confirms the measurements. These results further our understanding of nonlinear waves in silicon and open the way to soliton-based functionalities in complementary metal-oxide-semiconductor-compatible platforms. PMID:24423977
CHARACTERIZATION AND MODELING OF SOLITON TRANSMISSION AT 2.5 GB/S OVER 200 KM
Directory of Open Access Journals (Sweden)
KHALID A. S. AL-KHATEEB
2010-09-01
Full Text Available Soliton characteristics and soliton transmission have been simulated using a VPI simulator. Simulation was also used to construct and study a soliton communication system. Near soliton pulses emitted by an actively mode-locked laser is then compressed in a dispersion-compensating fiber (DCF to produce solitons. The effects of non-linearity and active pre-chirping of mode-locked laser diode sources were also investigated. Assessment on a modeled system using real data shows that propagation over 250 km at 2.5 Gb/s in standard fibers with 20 ps pulse widths is possible in the 1550 nm wavelength range.
Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Rasmussen, Kim; Henning, D.; Gabriel, H.
1996-01-01
We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...
Phase noise of dispersion-managed solitons
International Nuclear Information System (INIS)
Spiller, Elaine T.; Biondini, Gino
2009-01-01
We quantify noise-induced phase deviations of dispersion-managed solitons (DMS) in optical fiber communications and femtosecond lasers. We first develop a perturbation theory for the dispersion-managed nonlinear Schroedinger equation (DMNLSE) in order to compute the noise-induced mean and variance of the soliton parameters. We then use the analytical results to guide importance-sampled Monte Carlo simulations of the noise-driven DMNLSE. Comparison of these results with those from the original unaveraged governing equations confirms the validity of the DMNLSE as a model for many dispersion-managed systems and quantify the increased robustness of DMS with respect to noise-induced phase jitter.
Slunyaev, Alexey; Klein, Marco; Clauss, Günther F.
2016-04-01
Envelope soliton solutions are key elements governing the nonlinear wave dynamics within a simplified theory for unidirectional weakly modulated weakly nonlinear wave groups on the water surface. Within integrable models the solitons preserve their structure in collisions with other waves; they do not disperse and can carry energy infinitively long. Steep and short soliton-like wave groups have been shown to exist in laboratory tests [1] and, even earlier, in numerical simulations [2, 3]. Thus, long-living wave groups may play important role in the dynamics of intense sea waves and wave-structure interactions. The solitary wave groups may change the wave statistics and can be taken into account when developing approaches for the deterministic forecasting of dangerous waves, including so-called rogue waves. An experimental campaign has been conducted in the wave basin of the Technical University of Berlin on simulations of intense solitary wave groups. The first successful experimental observation of intense envelope solitons took place in this facility [1]. The new experiments aimed at following main goals: 1) to reproduce intense envelope solitons with different carrier wave lengths; 2) to estimate the rate of envelope soliton dissipation; 3) to consider the reflection of envelope solitons on a vertical wall; 4) to consider head-on collisions of envelope solitons, and 5) to consider overtaking interactions of envelope solitons. Up to 9 wave gauges were used in each experimental run, which enabled registration of the surface movement at different distances from the wavemaker, at different locations across the wave flume and near the wall. Besides surface displacements, the group envelope shapes were directly recorded, with use of phase shifts applied to the modulated waves generated by the wavemaker. [1] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105
Phononless soliton waves as early forerunners of crystalline material fracture
International Nuclear Information System (INIS)
Dubovskij, O.A.; Orlov, A.V.
2007-01-01
Phononless soliton waves of compression are shown to generate at a critical tension of crystals featuring real Lennard-Jones potential of interatomic interaction just before their fracture. A new method of nonlinear micro dynamics was applied to define the initial atomic displacements at high excitation energies. A solution is found that corresponds to a soliton wave running before the front of fracture. In a bounded crystal, the soliton being reflected from the crystal boundary passes the front of fracture and deforms while moving in the opposite direction. The amplitude and spectral characteristics of that type of soliton waves in crystals with a modified Lennard-Jones potential have been investigated. An approximate analytical solution was found for the soliton waves [ru
Wave Physics Oscillations - Solitons - Chaos
Nettel, Stephen
2009-01-01
This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior.
International Nuclear Information System (INIS)
Guo Rui; Tian Bo; Lue Xing; Zhang Haiqiang; Xu Tao
2010-01-01
For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium, a system of coupled equations is analytically studied in this paper. Painleve analysis shows that this system admits the Painleve property under some constraints. By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pair of this system is derived, and the Darboux transformation (DT) is constructed with the help of the obtained Lax pair. With symbolic computation, the soliton solutions are obtained by virtue of the DT algorithm. Figures are plotted to illustrate the dynamical features of the soliton solutions. Characteristics of the solitons propagating in an inhomogeneous multi-component nonlinear medium are discussed: (i) Propagation of one soliton and two-peak soliton; (ii) Elastic interactions of the parabolic two solitons; (iii) Overlap phenomenon between two solitons; (iv) Collision of two head-on solitons and two head-on two-peak solitons; (v) Two different types of interactions of the three solitons; (vi) Decomposition phenomenon of one soliton into two solitons. The results might be useful in the study on the ultrashort-pulse propagation in the inhomogeneous multi-component nonlinear media. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Soliton excitation in superlattice
International Nuclear Information System (INIS)
Mensah, S.Y.; Allotey, F.K.A.; Mensah, N.G.; Twum, A.K.
1995-10-01
Excitation of soliton in superlattice has been investigated theoretically. It is noted that the soliton velocity u and the length L depend on the amplitude E 0 and that an increase in the amplitude causes soliton width L to approach zero and the velocity u to that of light V in homogeneous medium. The characteristic parameters of soliton u, L and E 0 are related by expression u/L E 0 = ed/2(h/2π) which is constant depending only on the SL period d. It is observed also that the soliton has both energy E = 8V 2 (1 - u 2 /V 2 ) -1/2 and momentum P = u/V 2 E which makes it behave as relativistic free particle with rest energy 8V 2 . Its interaction with electrons can cause the soliton electric effect in SL. (author). 27 refs
Optical solitons and quasisolitons
International Nuclear Information System (INIS)
Zakharov, V.E.; Kuznetsov, E.A.
1998-01-01
Optical solitons and quasisolitons are investigated in reference to Cherenkov radiation. It is shown that both solitons and quasisolitons can exist, if the linear operator specifying their asymptotic behavior at infinity is sign-definite. In particular, the application of this criterion to stationary optical solitons shifts the soliton carrier frequency at which the first derivative of the dielectric constant with respect to the frequency vanishes. At that point the phase and group velocities coincide. Solitons and quasisolitons are absent, if the third-order dispersion is taken into account. The stability of a soliton is proved for fourth order dispersion using the sign-definiteness of the operator and integral estimates of the Sobolev type. This proof is based on the boundedness of the Hamiltonian for a fixed value of the pulse energy
Resonant trapping in the transport of a matter-wave soliton through a quantum well
International Nuclear Information System (INIS)
Ernst, Thomas; Brand, Joachim
2010-01-01
We theoretically investigate the scattering of bright solitons in a Bose-Einstein condensate on narrow attractive potential wells. Reflection, transmission, and trapping of an incident soliton are predicted to occur with remarkably abrupt transitions upon varying the potential depth. Numerical simulations of the nonlinear Schroedinger equation are complemented by a variational collective coordinate approach. The mechanism for nonlinear trapping is found to rely both on resonant interaction between the soliton and bound states in the potential well and on the radiation of small-amplitude waves. These results suggest that solitons can be used to probe bound states that are not accessible through scattering with single atoms.
Dynamics of surface solitons at the edge of chirped optical lattices
International Nuclear Information System (INIS)
Kartashov, Yaroslav V.; Torner, Lluis; Vysloukh, Victor A.
2007-01-01
We address soliton formation at the edge of chirped optical lattices imprinted in Kerr-type nonlinear media. We find families of power thresholdless surface waves that do not exist at other types of lattice interfaces. Such solitons form due to combined action of internal reflection at the interface, distributed Bragg-type reflection, and focusing nonlinearity. Remarkably, we discover that surfaces of chirped lattices are soliton attractors: Below an energy threshold, solitons launched well within the lattice self-bend toward the interface, and then stick to it
Stability of matter-wave solitons in optical lattices
Ali, Sk. Golam; Roy, S. K.; Talukdar, B.
2010-08-01
We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.
International Nuclear Information System (INIS)
Manciu, M.; Sen, S.; Hurd, A.J.
1999-01-01
The authors consider a chain of elastic (Hertzian) grains that repel upon contact according to the potential V = adelta u , u > 2, where delta is the overlap between the grains. They present numerical and analytical results to show that an impulse initiated at an end of a chain of Hertzian grains in contact eventually propagates as a soliton for all n > 2 and that no solitons are possible for n le 2. Unlike continuous, they find that colliding solitons in discrete media initiative multiple weak solitons at the point of crossing
International Nuclear Information System (INIS)
Rajasekaran, G.
1978-01-01
Recent developments in the theory of solitons and related objects in the fields of high energy physics and nuclear physics are reviewed. The aim is to concentrate on the physical aspects and explain why these objects have awakened the interest of physicists. The physics of solitons is discussed with the help of a simple one-dimensional soliton. Then the physically more interesting monopole-soliton is considered and its connection with the original Dirac monopole is pointed out. The ''revolutionary'' possibility of making fermions as composites of bosons is indicated. Both the one-dimensional solitons and the monopole-soliton are examples of ''topological solitons'' and the role of topology in the physics of solitons is explained. The possible importance of topological quantum numbers in providing a fundamental understanding of the basic conservation laws of physics is pointed out. Two examples of non-topological solitons namely, the nucleon as a bag of almost-massless quarks and the abnormal nucleons as a bag of almost massless nucleons is discussed. (auth.)
Preparing Schrodinger cat states by parametric pumping
Leghtas, Zaki; Touzard, Steven; Pop, Ioan; Vlastakis, Brian; Zalys-Geller, Evan; Albert, Victor V.; Jiang, Liang; Frunzio, Luigi; Schoelkopf, Robert J.; Mirrahimi, Mazyar; Devoret, Michel H.
2014-03-01
Maintaining a quantum superposition state of light in a cavity has important applications for quantum error correction. We present an experimental protocol based on parametric pumping and Josephson circuits, which could prepare a Schrodinger cat state in a cavity. This is achieved by engineering a dissipative environment, which exchanges only pairs or quadruples of photons with our cavity mode. The dissipative nature of this preparation would lead to the observation of a dynamical Zeno effect, where the competition between a coherent drive and the dissipation reveals non trivial dynamics. Work supported by: IARPA, ARO, and NSF.
Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations
Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)
1994-01-01
This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....
Large amplitude ion-acoustic solitons in dusty plasmas
International Nuclear Information System (INIS)
Tiwari, R. S.; Jain, S. L.; Mishra, M. K.
2011-01-01
Characteristics of ion-acoustic soliton in dusty plasma, including the dynamics of heavily charged massive dust grains, are investigated following the Sagdeev Potential formalism. Retaining fourth order nonlinearities of electric potential in the expansion of the Sagdeev Potential in the energy equation for a pseudo particle and integrating the resulting energy equation, large amplitude soliton solution is determined. Variation of amplitude (A), half width (W) at half maxima and the product P = AW 2 of the Korteweg-deVries (KdV), dressed and large amplitude soliton as a function of wide range of dust concentration are numerically studied for recently observed parameters of dusty plasmas. We have also presented the region of existence of large amplitude ion-acoustic soliton in the dusty plasma by analyzing the structure of the pseudo potential. It is found that in the presence of positively charged dust grains, system supports only compressive solitons, on the other hand, in the presence of negatively charged dust grains, the system supports compressive solitons up to certain critical concentration of dust grains and above this critical concentration, the system can support rarefactive solitons also. The effects of dust concentration, charge, and mass of the dust grains, on the characteristics of KdV, dressed and large amplitude the soliton, i.e., amplitude (A), half width at half maxima (W), and product of amplitude (A) and half width at half maxima (P = AW 2 ), are discussed in detail
Exact, multiple soliton solutions of the double sine Gordon equation
International Nuclear Information System (INIS)
Burt, P.B.
1978-01-01
Exact, particular solutions of the double sine Gordon equation in n dimensional space are constructed. Under certain restrictions these solutions are N solitons, where N <= 2q - 1 and q is the dimensionality of space-time. The method of solution, known as the base equation technique, relates solutions of nonlinear partial differential equations to solutions of linear partial differential equations. This method is reviewed and its applicability to the double sine Gordon equation shown explicitly. The N soliton solutions have the remarkable property that they collapse to a single soliton when the wave vectors are parallel. (author)
Soliton-type solutions for two models in mathematical physics
Al-Ghafri, K. S.
2018-04-01
In this paper, the generalised Klein-Gordon and Kadomtsov-Petviashvili Benjamin-Bona-Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions.
Soliton wave-speed management: Slowing, stopping, or reversing a solitary wave
Baines, Luke W. S.; Van Gorder, Robert A.
2018-06-01
While dispersion management is a well-known tool to control soliton properties such as shape or amplitude, far less effort has been directed toward the theoretical control of the soliton wave speed. However, recent experiments concerning the stopping or slowing of light demonstrate that the control of the soliton wave speed is of experimental interest. Motivated by these and other studies, we propose a management approach for modifying the wave speed of a soliton (or of other nonlinear wave solutions, such as periodic cnoidal waves) under the nonlinear Schrödinger equation. Making use of this approach, we are able to slow, stop, or even reverse a solitary wave, and we give several examples to bright solitons, dark solitons, and periodic wave trains, to demonstrate the method. An extension of the approach to spatially heterogeneous media, for which the wave may propagate differently at different spatial locations, is also discussed.
Sakkaravarthi, K; Kanna, T; Vijayajayanthi, M; Lakshmanan, M
2014-11-01
We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.
Matter-wave dark solitons in optical lattices
International Nuclear Information System (INIS)
Louis, Pearl J Y; Ostrovskaya, Elena A; Kivshar, Yuri S
2004-01-01
We analyse the Floquet-Bloch spectrum of matter waves in Bose-Einstein condensates loaded into single-periodic optical lattices and double-periodic superlattices. In the framework of the Gross-Pitaevskii equation, we describe the structure and analyse the mobility properties of matter-wave dark solitons residing on backgrounds of extended nonlinear Bloch-type states. We demonstrate that interactions between dark solitons can be effectively controlled in optical superlattices
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...
Indian Academy of Sciences (India)
The history leading to the discovery of soliton is interesting and impressive. The first documented observation of the solitary wave was made in 1834 by the .... Through the inverse scattering method, we are in a position to define the soliton in a rigorous manner. A transformation from the field variables to the scattering data is ...
Wakeless triple soliton accelerator
International Nuclear Information System (INIS)
Mima, K.; Ohsuga, T.; Takabe, H.; Nishihara, K.; Tajima, T.; Zaidman, E.; Horton, W.
1986-09-01
We introduce and analyze the concept of a wakeless triple soliton accelerator in a plasma fiber. Under appropriate conditions the triple soliton with two electromagnetic and one electrostatic waves in the beat-wave resonance propagates with velocity c leaving no plasma wake behind, while the phase velocity of the electrostatic wave is made also c in the fiber
Solitons as Newtonian particles
International Nuclear Information System (INIS)
Eboli, O.J.P.; Marques, G.C.
1982-07-01
The effect of external electromagnetic fields on non relativistic solitons is studied. Although the solitons are distorted by external fields, they still exhibit a Newtonian behavior. Some explicit examples of such a phenomenon are given, presenting solutions which exhibit Newtonian behavior for simple external fields. Furthermore, general results like charge and flux quantization are shown. (Author) [pt
Reflectionless discrete Schr\\"odinger operators are spectrally atypical
VandenBoom, Tom
2017-01-01
We prove that, if an isospectral torus contains a discrete Schr\\"odinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed intervals having capacity one are not the spectrum of any reflectionless discrete Schr\\"odinger operator. We also show that the only reflectionless discrete Schr\\"odinger operators having zero, one, or two spectral gaps are periodic.
Multiple soliton self-frequency shift cancellations in a temporally tailored photonic crystal fiber
Energy Technology Data Exchange (ETDEWEB)
Liu, Lai; Kang, Zhe; Li, Qing; Gao, Xuejian; Qin, Guanshi, E-mail: qings@jlu.edu.cn, E-mail: wpqin@jlu.edu.cn; Qin, Weiping, E-mail: qings@jlu.edu.cn, E-mail: wpqin@jlu.edu.cn [State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012 (China); Liao, Meisong; Hu, Lili [Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China); Ohishi, Yasutake [Research Center for Advanced Photon Technology, Toyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468-8511 (Japan)
2014-11-03
We report the generation of multiple soliton self-frequency shift cancellations in a temporally tailored tellurite photonic crystal fiber (PCF). The temporally regulated group velocity dispersion (GVD) is generated in the fiber by soliton induced optical Kerr effect. Two red-shifted dispersive waves spring up when two Raman solitons meet their own second zero-dispersion-wavelengths in the PCF. These results show how, through temporally tailored GVD, nonlinearities can be harnessed to generate unexpected effects.
Anderson localisation and optical-event horizons in rogue-soliton generation.
Saleh, Mohammed F; Conti, Claudio; Biancalana, Fabio
2017-03-06
We unveil the relation between the linear Anderson localisation process and nonlinear modulation instability. Anderson localised modes are formed in certain temporal intervals due to the random background noise. Such localised modes seed the formation of solitary waves that will appear during the modulation instability process at those preferred intervals. Afterwards, optical-event horizon effects between dispersive waves and solitons produce an artificial collective acceleration that favours the collision of solitons, which could eventually lead to a rogue-soliton generation.
Bose gas with two- and three-particle interaction: evolution of soliton-like bubbles
International Nuclear Information System (INIS)
Barashenkov, I.V.; Kholmurodov, Kh.T.
1988-01-01
Solutions of the non-linear Schroedinger equation (NSE) for the Bose gas with two- and three-particle interaction are considered. Problems of soliton-like bubble existence, stability and evolution of the moving soliton are studied. It is shown that at D=2.3 for low-amplitude waves propagating at the transonic velocity the NSE is reduced to a two- and three-dimensional Kadomtsev-Petviashvili (KP) equation and the NSE bubble soliton transfers to the KP one
The soliton solution of BBGKY quantum kinetic equations chain for different type particles system
International Nuclear Information System (INIS)
Rasulova, M.Yu.; Avazov, U.; Hassan, T.
2006-12-01
In the present paper on the basis of BBGKY chain of quantum kinetic equations the chain of equations for correlation matrices is derived, describing the evolution of a system of different types particles, which interact by pair potential. The series, which is the solution of this chain of equations for correlation matrices, is suggested. Using this series the solution of the last chain of equations is reduced to a solution of a set of homogeneous and nonhomogeneous von-Neumann's kinetic equations (analogue of Vlasov equations for quantum case). The first and second equations of this set of equations coincide with the first and second kinetic equations of the set, which is used in plasma physics. For an potential in the form of Dirac delta function, the solution of von-Neumann equation is defined through soliton solution of nonlinear Schrodinger equations. Based on von-Neumann equation one can define all terms of series, which is a solution of a chain of equations for correlation matrices. On the basis of these correlation matrices for a system of different types of particles we can define exact solution of BBGKY chain of quantum kinetic equations
Image denoising using the squared eigenfunctions of the Schrodinger operator
Kaisserli, Zineb; Laleg-Kirati, Taous-Meriem
2015-01-01
This study introduces a new image denoising method based on the spectral analysis of the semi-classical Schrodinger operator. The noisy image is considered as a potential of the Schrodinger operator, and the denoised image is reconstructed using the discrete spectrum of this operator. First results illustrating the performance of the proposed approach are presented and compared to the singular value decomposition method.
Newton-Cartan supergravity with torsion and Schrodinger supergravity
Bergshoeff, Eric; Rosseel, Jan; Zojer, Thomas
2015-01-01
We derive a torsionfull version of three-dimensional N - 2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The "superconformal" theory that we start with is Schrodinger supergravity which we obtain by gauging the Schrodinger superalgebra. We present
Image denoising using the squared eigenfunctions of the Schrodinger operator
Kaisserli, Zineb
2015-02-02
This study introduces a new image denoising method based on the spectral analysis of the semi-classical Schrodinger operator. The noisy image is considered as a potential of the Schrodinger operator, and the denoised image is reconstructed using the discrete spectrum of this operator. First results illustrating the performance of the proposed approach are presented and compared to the singular value decomposition method.
Schr"odinger's Unified Field Theory: Physics by Public Relations
Halpern, Paul
2009-05-01
We will explore the circumstances surrounding Erwin Schr"odinger's announcement in January 1947 that he had developed a comprehensive unified field theory of gravitation and electromagnetism. We will speculate on Schr"odinger's motivations for the mode and tone of his statements, consider the reaction of the international press within the context of the postwar era, and examine Einstein's response.
Soliton Coupling Driven by Phase Fluctuations in Auto-Parametric Resonance
Binder, B
2002-01-01
In this paper the interaction of sine-Gordon solitons and mediating linear waves is modelled by a special case of auto-parametric resonance, the Rayleigh-type self-excited non-linear autonomous system driven by a statistical phase gradient related to the soliton energy. Spherical symmetry can stimulate "whispering gallery modes" (WGM) with integral coupling number M=137.
Properties of bright solitons in averaged and unaveraged models for SDG fibres
Kumar, Ajit; Kumar, Atul
1996-04-01
Using the slowly varying envelope approximation and averaging over the fibre cross-section the evolution equation for optical pulses in semiconductor-doped glass (SDG) fibres is derived from the nonlinear wave equation. Bright soliton solutions of this equation are obtained numerically and their properties are studied and compared with those of the bright solitons in the unaveraged model.
Alteration of the soliton behavior in silica-fibers doped with passive resonant atoms
International Nuclear Information System (INIS)
Torres-Cisneros, G. E.; Nabiev, R.F.
1991-01-01
We have numerically studied for the first time the full dynamics describing the pulse propagation phenomenon in single-mode-silica-fibers doped with passive resonant two level atoms. For the specific case of a 3-order soliton we show that the inclusion of the resonant nonlinearities destroys the fundamental characteristics of the pulse soliton behavior. (Author)
Numerical study of properties of many-dimensional soliton-type objects
International Nuclear Information System (INIS)
Makhankov, V.G.; Shvachka, A.B.
1980-01-01
A brief review of the dynamical properties of many-dimensional quasi-solitons studied by means of the computer simulation in the framework of the nonlinear classical field theory models is presented. It is shown that the types of soliton interactions are model independent for studied models
Generation and dynamics of quadratic birefringent spatial gap solitons
International Nuclear Information System (INIS)
Anghel-Vasilescu, P.; Dorignac, J.; Geniet, F.; Leon, J.; Taki, A.
2011-01-01
A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe 2 (LGT) crystals. Once irradiated by a cw laser beam of 10 μm wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold.
Energy Technology Data Exchange (ETDEWEB)
Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)
2010-02-26
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
International Nuclear Information System (INIS)
Christian, J M; McDonald, G S; Chamorro-Posada, P
2010-01-01
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
International Nuclear Information System (INIS)
Carr, L.D.; Brand, J.
2004-01-01
It is shown that simultaneously changing the scattering length of an elongated, harmonically trapped Bose-Einstein condensate from positive to negative and inverting the axial portion of the trap, so that it becomes expulsive, results in a train of self-coherent solitonic pulses. Each pulse is itself a nondispersive attractive Bose-Einstein condensate that rapidly self-cools. The axial trap functions as a waveguide. The solitons can be made robustly stable with the right choice of trap geometry, number of atoms, and interaction strength. Theoretical and numerical evidence suggests that such a pulsed atomic soliton laser can be made in present experiments
Bifurcations and chaos of DNA solitonic dynamics
International Nuclear Information System (INIS)
Gonzalez, J.A.; Martin-Landrove, M.; Carbo, J.R.; Chacon, M.
1994-09-01
We investigated the nonlinear DNA torsional equations proposed by Yakushevich in the presence of damping and external torques. Analytical expressions for some solutions are obtained in the case of the isolated chain. Special attention is paid to the stability of the solutions and the range of soliton interaction in the general case. The bifurcation analysis is performed and prediction of chaos is obtained for some set of parameters. Some biological implications are suggested. (author). 11 refs, 13 figs
Soliton solutions in a diatomic lattice system
International Nuclear Information System (INIS)
Yajima, Nobuo; Satsuma, Junkichi.
1979-04-01
A continuum limit is considered for a diatomic lattice system with a cubic nonlinearity. A long wave equation describing the interaction of acoustic and optical modes is obtained. It reduces, in certain approximations, to equations having coupled wave solutions. The solutions exhibit trapping of an optical mode by an acoustic soliton. The form of the trapped optical wave depends on the mass ratio of adjacent particles in the diatomic lattice. (author)
Topological solitons in 8-spinor mie electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Rybakov, Yu. P., E-mail: soliton4@mail.ru [Peoples' Friendship University of Russia, Department of Theoretical Physics (Russian Federation)
2013-10-15
We investigate the effective 8-spinor field model suggested earlier as the generalization of nonlinear Mie electrodynamics. We first study in pure spinorial model the existence of topological solitons endowed with the nontrivial Hopf invariant Q{sub H}, which can be interpreted as the lepton number. Electromagnetic field being included as the perturbation, we estimate the energy and the spin of the localized charged configuration.
International Nuclear Information System (INIS)
Yong Chen; Qi Wang
2005-01-01
In this paper, we extend the algebraic method proposed by Fan (Chaos, Solitons and Fractals 20 (2004) 609) and the improved extended tanh method by Yomba (Chaos, Solitons and Fractals 20 (2004) 1135) to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). Some new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation are obtained
Soliton patterns and breakup thresholds in hydrogen-bonded chains
International Nuclear Information System (INIS)
Tchakoutio Nguetcho, A.S.; Kofane, T.C.
2006-12-01
We study the dynamics of protons in hydrogen-bonded quasi one-dimensional networks in terms of a diatomic lattice model of protons and heavy ions, with a phi-four on-site substrate potential. We show that the model with linear and nonlinear coupling between lattice sites of the quartic type for the protons admits a richer dynamics that cannot be found with linear coupling. Depending on the two types of physical boundary conditions namely, the drop and condensate types of boundary conditions, and on conditions that require the presence of linear and nonlinear dispersion terms, soliton patterns that are represented by soliton with compact support, peak, drop, bell, cusp, shock, kink, bubble and loop solitons, are derived within a continuum approximation. The phase trajectories, as well as an analytical analysis, provide information on an disintegration of soliton patterns upon reaching some critical values of the lattice parameters. The total energies of soliton patterns are exactly calculated in the displacive limit. We also show that when the phonon anharmonism is taken into account, the width and the energy of soliton patterns are in qualitative agreement with experimental data. (author)
Stability of line solitons for the KP-II equation in R2
Mizumachi, Tetsu
2015-01-01
The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as x\\to\\infty. He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward y=\\pm\\infty. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.
International Nuclear Information System (INIS)
Adhikari, Sadhan K.
2005-01-01
We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schroedinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type
Coupled matter-wave solitons in optical lattices
Golam Ali, Sk; Talukdar, B.
2009-06-01
We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (Veff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well Veff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of Veff(LOL) increases as k increases and that of Veff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution
Coupled matter-wave solitons in optical lattices
International Nuclear Information System (INIS)
Golam Ali, Sk; Talukdar, B.
2009-01-01
We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (V eff (NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well V eff (LOL). But these effective potentials have opposite k dependence in the sense that the depth of V eff (LOL) increases as k increases and that of V eff (NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during
Bistable dark solitons of a cubic-quintic Helmholtz equation
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2010-01-01
We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.
Relativistic solitons and pulsars
Energy Technology Data Exchange (ETDEWEB)
Karpman, V I [Inst. of Terrestrial Magnetism, Ionosphere, and Radio-Wave Propagation, Moscow; Norman, C A; ter Haar, D; Tsytovich, V N
1975-05-01
A production mechanism for stable electron bunches or sheets of localized electric fields is investigated which may account for pulsar radio emission. Possible soliton phenomena in a one-dimensional relativistic plasma are analyzed, and it is suggested that the motion of a relativistic soliton, or ''relaton'', along a curved magnetic-field line may produce radio emission with the correct polarization properties. A general MHD solution is obtained for relatons, the radiation produced by a relativistic particle colliding with a soliton is evaluated, and the emission by a soliton moving along a curved field line is estimated. It is noted that due to a number of severe physical restrictions, curvature radiation is not a very likely solution to the problem of pulsar radio emission. (IAA)
International Nuclear Information System (INIS)
Swieca, J.A.
1976-01-01
Some aspects of two recent developments in quantum field theory are discussed. First, related with 'extended particles' such as soliton, kink and the 't Hooft monopole. Second, with confinement of particles which are realized in the Schwinger model [pt
Perturbed soliton excitations in inhomogeneous DNA
International Nuclear Information System (INIS)
Daniel, M.; Vasumathi, V.
2005-05-01
We study nonlinear dynamics of inhomogeneous DNA double helical chain under dynamic plane-base rotator model by considering angular rotation of bases in a plane normal to the helical axis. The DNA dynamics in this case is found to be governed by a perturbed sine-Gordon equation when taking into account the interstrand hydrogen bonding energy and intrastrand inhomogeneous stacking energy and making an analogy with the Heisenberg model of the Hamiltonian for an inhomogeneous anisotropic spin ladder with ferromagnetic legs and antiferromagentic rung coupling. In the homogeneous limit the dynamics is governed by the kink-antikink soliton of the sine-Gordon equation which represents the formation of open state configuration in DNA double helix. The effect of inhomogeneity in stacking energy in the form of localized and periodic variations on the formation of open states in DNA is studied under perturbation. The perturbed soliton is obtained using a multiple scale soliton perturbation theory by solving the associated linear eigen value problem and constructing the complete set of eigen functions. The inhomogeneity in stacking energy is found to modulate the width and speed of the soliton depending on the nature of inhomogeneity. Also it introduces fluctuations in the form of train of pulses or periodic oscillation in the open state configuration (author)
Solitons in a relativistic plasma with negative ions--
International Nuclear Information System (INIS)
Das, G.C.; Karmakar, B.; Ibohanbi Singh, KH.
1990-01-01
The interaction of the nonlinearity and the dispersiveness causing the solitary waves are studied in a relativistic plasma with negative ions through the derivation of a nonlinear partial differential equation known as the Korteweg-Devries (K-DV) equation. The negative ions play a salient feature on the existence and behavior of the solitons and could be of interest in laboratory plasmas. First, the observations are made in a nonisothermal plasma, and later the reduction to the nonisothermality of the plasma shows entirely different characteristics as compared to the solitons in the isothermal plasmas. A comparison with the various solutions has been emphasized
Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
Ming, Yi; Ye, Liu; Chen, Han-Shuang; Mao, Shi-Feng; Li, Hui-Min; Ding, Ze-Jun
2018-01-01
Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-β lattices and the asymmetric Fermi-Pasta-Ulam-α β lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.
Fate of a gray soliton in a quenched Bose-Einstein condensate
Gamayun, O.; Bezvershenko, Yu. V.; Cheianov, V.
2015-03-01
We investigate the destiny of a gray soliton in a repulsive one-dimensional Bose-Einstein condensate undergoing a sudden quench of the nonlinearity parameter. The outcome of the quench is found to depend dramatically on the ratio η of the final and initial values of the speed of sound. For integer η the soliton splits into exactly 2 η -1 solitons. For noninteger η the soliton decays into multiple solitons and Bogoliubov modes. The case of integer η is analyzed in detail. The parameters of solitons in the out state are found explicitly. Our approach exploits the inverse scattering method and can be easily used for similar quenches in any classical integrable system.
The fate of a gray soliton in a quenched Bose-Einstein condensate
Gamayun, Oleksandr; Bezvershenko, Yulia; Cheianov, Vadim
2015-03-01
We investigate the destiny of a gray soliton in a repulsive one-dimensional Bose-Einstein condensate undergoing a sudden quench of the non-linearity parameter. The outcome of the quench is found to depend dramatically on the ratio η of the final and initial values of the speed of sound. For integer η the soliton splits into exactly 2 η - 1 solitons. For non-integer η the soliton decays into multiple solitons and Bogoliubov modes. The case of integer η is analyzed in detail. The parameters of solitons in the out-state are found explicitly. Our approach exploits the inverse scattering method and can be easily used for the similar quenches in any classical integrable system.
Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates
International Nuclear Information System (INIS)
Theocharis, G.; Kevrekidis, P. G.; Weller, A.; Ronzheimer, J. P.; Gross, C.; Oberthaler, M. K.; Frantzeskakis, D. J.
2010-01-01
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.
Slow-light solitons in atomic media and doped optical fibers
International Nuclear Information System (INIS)
Korolkova, N.; Sinclair, G.F.; Leonhardt, U.
2005-01-01
Full text: We show how to generate optical solitons in atomic media that can be slowed down or accelerated at will. Such slow-light soliton is a polarization structure propagating with a speed that is proportional to the total intensity of the incident light. Ultimately, this method will allow the storage, retrieval and possibly the manipulation of the quantum information in atomic media. Solitons with controllable speed are constructed generalizing the theory of slow-light propagation to an integrable regime of nonlinear dynamics. For the first time, the inverse scattering method for slow-light solitons is developed. In contrast to the pioneering experimental demonstrations of slow light, we consider strong spin modulations where the non-linear dynamics of light and atoms creates polarization solitons. We also analyze how this scheme can be implemented in optical fibers doped with Lambda-atoms. In quantum-information applications, such slow-light solitons could complement the use of quantum solitons in fibres with the advantage of storing quantum information in media and complement methods for quantum memory with the advantages of non-linear dynamics, in particular the intrinsic stability of solitons. (author)
A soliton perturbation scheme for 3x3 inverse scattering transform
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Banerjee, R.S.; Roy, T.
1979-01-01
A perturbation method for the soliton solutions of nonlinear equations tractable using 3x3 matrix IST formalism is discussed in detait. The corresponding changes in conservation laws are also considered. (author)
International Nuclear Information System (INIS)
Brand, Joachim; Reinhardt, William P.
2002-01-01
The connection between quantized vortices and dark solitons in a waveguidelike trap geometry is explored in the framework of the nonlinear Schroedinger equation. Variation of the transverse confinement leads from the quasi-one-dimensional (1D) regime, where solitons are stable, to 2D (or 3D) confinement, where soliton stripes are subject to a transverse modulational instability known as the 'snake instability'. We present numerical evidence of a regime of intermediate confinement where solitons decay into single, deformed vortices with solitonic properties rather than vortex pairs as associated with the 'snake' metaphor. Further relaxing the transverse confinement leads to the production of two and then three vortices, which correlates perfectly with a Bogoliubov stability analysis. The decay of a stationary dark soliton (or, planar node) into a single solitonic vortex is predicted to be experimentally observable in a 3D harmonically confined dilute-gas Bose-Einstein condensate
Probe-controlled soliton frequency shift in the regime of optical event horizon.
Gu, Jie; Guo, Hairun; Wang, Shaofei; Zeng, Xianglong
2015-08-24
In optical analogy of the event horizon, temporal pulse collision and mutual interactions are mainly between an intense solitary wave (soliton) and a dispersive probe wave. In such a regime, here we numerically investigate the probe-controlled soliton frequency shift as well as the soliton self-compression. In particular, in the dispersion landscape with multiple zero dispersion wavelengths, bi-directional soliton spectral tunneling effects is possible. Moreover, we propose a mid-infrared soliton self-compression to the generation of few-cycle ultrashort pulses, in a bulk of quadratic nonlinear crystals in contrast to optical fibers or cubic nonlinear media, which could contribute to the community with a simple and flexible method to experimental implementations.
Soliton on thin vortex filament
International Nuclear Information System (INIS)
Konno, Kimiaki; Mituhashi, Masahiko; Ichikawa, Y.H.
1990-12-01
Showing that one of the equations found by Wadati, Konno and Ichikawa is equivalent to the equation of motion of a thin vortex filament, we investigate solitons on the vortex filament. N vortex soliton solution is given in terms of the inverse scattering method. We examine two soliton collision processes on the filament. Our analysis provides the theoretical foundation of two soliton collision processes observed numerically by Aref and Flinchem. (author)
Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng
2004-01-01
Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair
International Nuclear Information System (INIS)
Adam, C.; Haberichter, M.; Wereszczynski, A.
2016-01-01
There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly coincides with the thermodynamical or continuum-mechanical volume. In addition, this volume may be defined uniquely for rather arbitrary solitons in arbitrary dimensions.
Energy Technology Data Exchange (ETDEWEB)
Adam, C., E-mail: adam@fpaxp1.usc.es [Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela (Spain); Haberichter, M. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Wereszczynski, A. [Institute of Physics, Jagiellonian University, Lojasiewicza 11, Kraków (Poland)
2016-03-10
There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly coincides with the thermodynamical or continuum-mechanical volume. In addition, this volume may be defined uniquely for rather arbitrary solitons in arbitrary dimensions.
Transverse stability of Kawahara solitons
DEFF Research Database (Denmark)
Karpman, V.I.
1993-01-01
The transverse stability of the planar solitons described by the fifth-order Korteweg-de Vries equation (Kawahara solitons) is studied. It is shown that the planar solitons are unstable with respect to bending if the coefficient at the fifth-derivative term is positive and stable if it is negative...
Optical soliton communication using ultra-short pulses
Sadegh Amiri, Iraj
2015-01-01
This brief analyzes the characteristics of a microring resonator (MRR) to perform communication using ultra-short soliton pulses. The raising of nonlinear refractive indices, coupling coefficients and radius of the single microring resonator leads to decrease in input power and round trips wherein the bifurcation occurs. As a result, bifurcation or chaos behaviors are seen at lower input power of 44 W, where the nonlinear refractive index is n2=3.2×10−20 m2/W. Using a decimal convertor system, these ultra-short signals can be converted into quantum information. Results show that multi solitons with FWHM and FSR of 10 pm and 600 pm can be generated respectively. The multi optical soliton with FWHM and FSR of 325 pm and 880 nm can be incorporated with a time division multiple access (TDMA) system wherein the transportation of quantum information is performed.
Massively Parallel Algorithms for Solution of Schrodinger Equation
Fijany, Amir; Barhen, Jacob; Toomerian, Nikzad
1994-01-01
In this paper massively parallel algorithms for solution of Schrodinger equation are developed. Our results clearly indicate that the Crank-Nicolson method, in addition to its excellent numerical properties, is also highly suitable for massively parallel computation.
Parametrically tunable soliton-induced resonant radiation by three-wave mixing
DEFF Research Database (Denmark)
Zhou, Binbin; Liu, Xing; Guo, Hairun
2017-01-01
We show that a temporal soliton can induce resonant radiation by three-wave mixing nonlinearities. This constitutes a new class of resonant radiation whose spectral positions are parametrically tunable. The experimental verification is done in a periodically poled lithium niobate crystal, where...... a femtosecond near-IR soliton is excited and resonant radiation waves are observed exactly at the calculated soliton phasematching wavelengths via the sum- and difference-frequency generation nonlinearities. This extends the supercontinuum bandwidth well into the mid IR to span 550–5000 nm, and the mid-IR edge...
Infinitely many solutions for fractional Schr\\"odinger equations in R^N
Directory of Open Access Journals (Sweden)
Caisheng Chen
2016-03-01
Full Text Available Using variational methods we prove the existence of infinitely many solutions to the fractional Schrodinger equation $$ (-\\Delta^su+V(xu=f(x,u, \\quad x\\in\\mathbb{R}^N, $$ where $N\\ge 2, s\\in (0,1$. $(-\\Delta^s$ stands for the fractional Laplacian. The potential function satisfies $V(x\\geq V_0>0$. The nonlinearity f(x,u is superlinear, has subcritical growth in u, and may or may not satisfy the (AR condition.
Double symmetry breaking of solitons in one-dimensional virtual photonic crystals
International Nuclear Information System (INIS)
Li Yongyao; Malomed, Boris A.; Feng Mingneng; Zhou Jianying
2011-01-01
We demonstrate that spatial solitons undergo two consecutive spontaneous symmetry breakings (SSBs), with the increase of the total power, in nonlinear photonic crystals (PhCs) built as arrays of alternating linear and nonlinear stripes, in the case when the maxima of the effective refractive index coincide with the minima of the self-focusing coefficient and vice versa (i.e., the corresponding linear and nonlinear periodic potentials are in competition). This setting may be induced, as a virtual PhC, by means of the electromagnetically induced-transparency (EIT) technique, in a uniform optical medium. It may also be realized as a Bose-Einstein condensate (BEC) subject to the action of the combined periodic optical potential and periodically modulated Feshbach resonance. The first SSB happens at the center of a linear stripe, pushing a broad low-power soliton into an adjacent nonlinear stripe and gradually suppressing side peaks in the soliton's shape. Then the soliton restores its symmetry, being pinned to the midpoint of the nonlinear stripe. The second SSB occurs at higher powers, pushing the narrow soliton off the center of the nonlinear channel, while the soliton keeps its internal symmetry. The results are obtained by means of numerical and analytical methods. They may be employed to control switching of light beams by means of the varying power.
Non-topological soliton bag model
International Nuclear Information System (INIS)
Wilets, L.
1986-01-01
The Friedberg-Lee soliton model, which effects confinement by a quantal scalar field, is discussed. The Lagrangian for the non-topological soliton model is the usual QCD Lagrangian supplemented by a non-linear scalar sigma field term. Static solutions to the field equations are considered in the mean field approximation. Small amplitude oscillations are discussed. Quantum alternatives to the mean field approximation are also considered. Methods of momentum projection and Lorentz boost are described, and the generator coordinate method is discussed. Calculations of the N-N interaction are reviewed briefly. Also discussed is one-gluon exchange, as well as the pion and dressing of the baryons. The hadron states are summarized. One loop quantum corrections are discussed briefly. Work in progress is mentioned in the areas of N-anti N annihilation, the many bag problem, and a Pauli equation for the nucleon. 31 refs
Directory of Open Access Journals (Sweden)
Kilic Bulent
2016-01-01
Full Text Available This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE with time dependent coefficients.
A new six-component super soliton hierarchy and its self-consistent sources and conservation laws
International Nuclear Information System (INIS)
Wei Han-yu; Xia Tie-cheng
2016-01-01
A new six-component super soliton hierarchy is obtained based on matrix Lie super algebras. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy. After that, the self-consistent sources of the new six-component super soliton hierarchy are presented. Furthermore, we establish the infinitely many conservation laws for the integrable super soliton hierarchy. (paper)
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.
Directory of Open Access Journals (Sweden)
A. V. Shapovalov
2018-02-01
Full Text Available This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics and related to biological systems, that focus on how small impacts can significantly change the state of the system at large spatial scales. This problem is very extensive, and it cannot be fully resolved in this paper. Instead, some selected physical effects are briefly reviewed. We consider sine-Gordon solitons and nonlinear Schrodinger solitons in some models of DNA as examples of self-organization at the molecular level, as well as examine features of their formation and dynamics under the influence of external influences. In addition, the formation of patterns in the generalized Fisher–KPP model is viewed as a simple example of self-organization in a system with nonlocal interaction at the cellular level. Symmetries of model equations are employed to analyze the considered nonlinear phenomena. In this context the possible relations between phenomena considered and released activity effect, which is assessed differently in the literature, are discussed.
Baryon considered as a soliton in loop space
International Nuclear Information System (INIS)
Kazakov, V.A.; Migdal, A.A.
1981-01-01
The baryon mass for large N is expressed in QCD in terms of the collective field in loop space, which satisfies the nonlinear functional-integral equation. This collective loop field is a relativistic generalization of the self-consistent Witten field. Our approach confirms Witten's idea that a baryon is a soliton in 1/N expansion
Phase conjugation of gap solitons: A numerical study
Indian Academy of Sciences (India)
We study the effect of a nearby phase-conjugate mirror (PCM) on the gap soliton of a. Kerr non-linear ... They are characterized by a sech field distribution corresponding to the ... It is a generalization of the earlier model proposed by Jose et.
International Nuclear Information System (INIS)
Boya, L.J.; Carinena, J.F.; Mateos, J.
1978-01-01
Starting from classical field theory with a Lagrangian, solitons are identified with solutions of the field equations which satisfy peculiar boundary conditions. The symmetry group which causes the degenerate vacuum is taken generally internal, that is, not operating in space-time. Gauge symmetry plays a dominant role. A precise definition of solitons is given and it is shown how to study some continuous mappings of the ''distant'' parts of space on the set of degenerate vacua. A marvellous instrument, the exact homotopy sequence, is applied to calculate homotopy groups of some higher-dimensional manifolds
General N-Dark Soliton Solutions of the Multi-Component Mel'nikov System
Han, Zhong; Chen, Yong; Chen, Junchao
2017-07-01
A general form of N-dark soliton solutions of the multi-component Mel'nikov system are presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general N-dark-dark soliton solutions in Gram determinant form are constructed through the KP hierarchy reduction method. The dynamics of single dark-dark soliton and two dark-dark solitons are discussed in detail. It can be shown that the collisions of dark-dark solitons are elastic and energies of the solitons in different components completely transmit through. In addition, the dark-dark soliton bound states including both stationary and moving cases are also investigated. An interesting feature for the coupled Mel'nikov system is that the stationary dark-dark soliton bound states can exist for all possible combinations of nonlinearity coefficients including positive, negative and mixed types, while the moving case are possible when nonlinearity coefficients take opposite signs or they are both negative.
Black holes will break up solitons and white holes may destroy them
International Nuclear Information System (INIS)
Akbar, Fiki T.; Gunara, Bobby E.; Susanto, Hadi
2017-01-01
Highlights: • What happens if a soliton collides with a black or white hole? • Solitons can pass through black hole horizons, but they will break up into several solitons after the collision. • In the interaction with a white hole horizon, solitons either pass through the horizon or will be destroyed by it. - Abstract: We consider a quantum analogue of black holes and white holes using Bose–Einstein condensates. The model is described by the nonlinear Schrödinger equation with a ‘stream flow’ potential, that induces a spatial translation to standing waves. We then mainly consider the dynamics of dark solitons in a black hole or white hole flow analogue and their interactions with the event horizon. A reduced equation describing the position of the dark solitons was obtained using variational method. Through numerical computations and comparisons with the analytical approximation we show that solitons can pass through black hole horizons even though they will break up into several solitons after the collision. In the interaction with a white hole horizon, we show that solitons either pass through the horizon or will be destroyed by it.
Black holes will break up solitons and white holes may destroy them
Energy Technology Data Exchange (ETDEWEB)
Akbar, Fiki T., E-mail: ftakbar@fi.itb.ac.id [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha no. 10, Bandung, 40132 (Indonesia); Gunara, Bobby E., E-mail: bobby@fi.itb.ac.id [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha no. 10, Bandung, 40132 (Indonesia); Susanto, Hadi, E-mail: hsusanto@essex.ac.uk [Department of Mathematical Sciences, University of Essex, Colchester, CO4 3SQ (United Kingdom)
2017-06-15
Highlights: • What happens if a soliton collides with a black or white hole? • Solitons can pass through black hole horizons, but they will break up into several solitons after the collision. • In the interaction with a white hole horizon, solitons either pass through the horizon or will be destroyed by it. - Abstract: We consider a quantum analogue of black holes and white holes using Bose–Einstein condensates. The model is described by the nonlinear Schrödinger equation with a ‘stream flow’ potential, that induces a spatial translation to standing waves. We then mainly consider the dynamics of dark solitons in a black hole or white hole flow analogue and their interactions with the event horizon. A reduced equation describing the position of the dark solitons was obtained using variational method. Through numerical computations and comparisons with the analytical approximation we show that solitons can pass through black hole horizons even though they will break up into several solitons after the collision. In the interaction with a white hole horizon, we show that solitons either pass through the horizon or will be destroyed by it.
Real and virtual multidimensional solitons
International Nuclear Information System (INIS)
Boiti, M.; Martina, L.; Pashaev, O.K.; Pempinelli, F.
1993-01-01
Recently it has been shown that in two spatial and one temporal dimensions (2+1) there exist localized solitons. These coherent structures display a richer phenomenology than the one dimensional solitons. Different effects have been reported successively in a series of papers. Some of them are due to the fact that the soliton solution is structurally unstable with respect to special choices of the parameters. Also some quantum-like effects as the non conservation of the number of solitons have been discovered by using direct methods. This report is dedicated to the study of the origin and generality of these new effects in the context of the Spectral Transform (ST) theory. By choosing more general boundaries than those used in previous papers we derive an N 2 -soliton solution, which is parameterized by a point in a space of 4N(N+1) real parameters. Of these parameters 2N(N+2) are determined by the choice of the boundaries and fix the velocity and the possible location of the solitons in the plane at large times, while the remaining 2N govern the dynamics of the solitons during the interaction. The total mass of solitons is conserved but, in general, the mass of the single soliton is not preserved by the interaction. The extreme cases in which the masses of one or more solitons are zero at t = -∞ or/and t = +∞ are also allowed. We call these solitons with asymptotic zero masses and, consequently, with asymptotic zero amplitudes virtual solitons. The total momentum of solitons is not conserved because the boundaries act as external forces. Solitons can simulate inelastic scattering processes of quantum particles including creation and annihilation of particles
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Spherical solitons in Earth’S mesosphere plasma
International Nuclear Information System (INIS)
Annou, K.; Annou, R.
2016-01-01
Soliton formation in Earth’s mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev–Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry
Coherent structures amidst chaos: Solitons, fronts, and vortices
International Nuclear Information System (INIS)
Campbell, D.K.
1996-01-01
I introduce the concept of open-quote open-quote coherent structures close-quote close-quote emdash localized, persistent, propagating nonlinear waves emdash and argue that they are ubiquitous in spatially extended nonlinear systems. I discuss various specific forms of coherent structures emdash solitons, wave fronts, vortices emdash and illustrate how they arise in physics, chemistry, biology, and physiology. copyright 1996 American Institute of Physics
Spatial Discrete Soliton in Two dimensional with Kerr medium
International Nuclear Information System (INIS)
Aghdami, M.; Mostafavi, D.; Mokhtari, F.; Keradmand, R.
2012-01-01
In this theoretical work propagation of the Gaussian beam through a two dimensional waveguides array is numerically investigated, in which each waveguide contains medium with Kerr nonlinearity considering coupling to vertical, horizontal and diagonal neighbor through light electric field. Different values of intensity, nonlinear coefficient Kerr and Gaussian beam width of incident Gaussian beam are examined and finally suitable parameters for providing central spatial solitons are obtained.
The nontopological soliton model
International Nuclear Information System (INIS)
Wilets, L.
1988-01-01
The nontopological soliton model introduced by Friedberg and Lee, and variations of it, provide a method for modeling QCD which can effectively include the dynamics of hadronic collisions as well as spectra. Absolute color confinement is effected by the assumed dielectric properties of the medium. A recently proposed version of the model is chirally invariant. 32 refs., 5 figs., 1 tab
International Nuclear Information System (INIS)
Wilets, L.; Bickeboeller, M.; Birse, M.C.
1985-01-01
A summary of recent and current research on the Soliton Bag Model is presented. The unique feature of the model, namely dynamics, is emphasized, since this permits calculation of reactions within the framework of a covariant effective Lagrangian. One gluon exchange effects are included. 17 refs., 3 figs
Statistical mechanics of solitons
International Nuclear Information System (INIS)
Bishop, A.
1980-01-01
The status of statistical mechanics theory (classical and quantum, statics and dynamics) is reviewed for 1-D soliton or solitary-wave-bearing systems. Primary attention is given to (i) perspective for existing results with evaluation and representative literature guide; (ii) motivation and status report for remaining problems; (iii) discussion of connections with other 1-D topics
Engineering of spatial solitons in two-period QPM structures
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Carrasco, Silvia; Torner, Lluis
2002-01-01
We report on a scheme which might make it practically possible to engineer the effective competing nonlinearities that on average govern the light propagation in quasi-phase-matching (QPM) gratings. Modulation of the QPM period with a second longer period, introduces an extra degree of freedom...... relative lengths of the two periods and we consider the effect on solitons and the bandwidth for their generation. We derive an expression for the bandwidth of multicolor soliton generation in two-period QPM samples and we predict and confirm numerically that the bandwidth is broader in the two-period QPM...
A fluid dynamic approach to the dust-acoustic soliton
International Nuclear Information System (INIS)
McKenzie, J.F.; Doyle, T.B.
2002-01-01
The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave
A Fluid Dynamic Approach to the Dust-Acoustic Soliton
McKenzie, J. F.; Doyle, T. B.
2002-12-01
The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave.
Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref
2017-11-01
This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.
Two-dimensional behavior of solitons in a low-β plasma with convective motion
International Nuclear Information System (INIS)
Makino, Mitsuhiro; Kamimura, Tetsuo; Sato, Tetsuya.
1981-01-01
The initial value problem of the Hasegawa-Mima (HM) equation, which describes the propagation of drift waves in a low beta magnetized plasma, is numerically studied. Solitons are formed from an initial sinusoidal wave. For a wide range of initial conditions, the number of solitons and the recurrence time agree well with those obtained from the KdV eq. reduced from the HM eq. by Nozaki et al. As a result of nonlinear interactions among different solitons, their peak positions shift in the direction normal to the zeroth order convective motion in a regular but different fashion. When we start from a sinusoidal wave, the peaks of the generated soliton train line up on a line at an angle with respect to the convective direction. Two-deimensional collisions of different solitons are examined. (author)
Magnetization Reversal through Soliton in a Site-Dependent Weak Ferromagnet
International Nuclear Information System (INIS)
Kavitha, L.; Sathishkumar, P.; Saravanan, M.; Gopi, D.
2010-06-01
Switching the magnetization of a magnetic bit through flipping of soliton offers the possibility of developing a new innovative approach for data storage technologies. The spin dynamics of a site-dependent ferromagnet with antisymmetric Dzyaloshinskii-Moriya interaction is governed by a generalized inhomogeneous higher order nonlinear Schroedinger equation. We demonstrate the magnetization reversal through flipping of soliton in the ferromagnetic medium by solving the two coupled evolution equations for the velocity and amplitude of the soliton using the fourth order Runge-Kutta method numerically. We propose a new approach to induce the flipping behaviour of soliton in the presence of inhomogeneity by tuning the parameter associated with Dzyaloshinskii-Moriya interaction which causes the soliton to move with constant velocity and amplitude along the spin lattice. (author)
International Nuclear Information System (INIS)
Liu Xueming
2011-01-01
The soliton formation and evolution are numerically and experimentally investigated in passively-mode-locked lasers where pulses encounter ultralong anomalous-dispersion fibers. The pulse formation and evolution in lasers are determined by two balances, namely, nonlinearity and anomalous-dispersion balance and intracavity filtering and self-amplitude modulation balance. It is numerically found that a higher-energy soliton can be split into identical lower-energy multisolitons with exactly the same physical properties. Simulation results show that the separation of neighboring solitons is variational in the temporal domain. The temporal and spectral characteristics of solitons have large variations throughout the laser cavity, qualitatively distinct from the steady state of conventional solitons. The experimental observations confirm the theoretical predictions.
Oscillating electromagnetic soliton in an anisotropic ferromagnetic medium
Energy Technology Data Exchange (ETDEWEB)
Sathishkumar, P., E-mail: perumal_sathish@yahoo.co.in [Department of Physics, K.S.R. College of Engineering (Autonomous), Tiruchengode 637215, Tamilnadu (India); Senjudarvannan, R. [Department of Physics, Jansons Institute of Technology, Karumathampatty, Coimbatore 641659 (India)
2017-05-01
We investigate theoretically the propagation of electromagnetic oscillating soliton in the form of breather in an anisotropic ferromagnetic medium. The interaction of magnetization with the magnetic field component of the electromagnetic (EM) wave has been studied by solving Maxwell's equations coupled with a Landau–Lifshitz equation for the magnetization of the medium. We made a small perturbation on the magnetization and magnetic field along the direction of propagation of EM wave in the framework of reductive perturbation method and the associated nonlinear magnetization dynamics is governed by a generalized derivative nonlinear Schrödinger (DNLS) equation. In order to understand the dynamics of the concerned system, we employ the Jacobi elliptic function method to solve the DNLS equation and deduce breatherlike soliton modes for the EM wave in the medium. - Highlights: • The propagation of electromagnetic oscillating soliton in an anisotropic ferromagnetic medium is investigated in the presence of varying external magnetic field. • The magnetization and electromagnetic wave modulates in the form of breathing like oscillating solitons. • The governing nonlinear spin dynamical equation is studied through a reductive perturbation method. • The magnetization components of the ferromagnetic medium are derived using Jacobi elliptic functions method with the aid of symbolic computation.
Phase locking between Josephson soliton oscillators
DEFF Research Database (Denmark)
Holst, T.; Hansen, Jørn Bindslev; Grønbech-Jensen, N.
1990-01-01
We report observations of phase-locking phenomena between two Josephson soliton (fluxon) oscillators biased in self-resonant modes. The locking strength was measured as a function of bias conditions. A frequency tunability of the phase-locked oscillators up to 7% at 10 GHz was observed. Two coupled...... perturbed sine-Gordon equations were derived from an equivalent circuit consisting of inductively coupled, nonlinear, lossy transmission lines. These equations were solved numerically to find the locking regions. Good qualitative agreement was found between the experimental results and the calculations...
Trofimov, Vyacheslav A.; Lysak, Tatiana M.
2018-04-01
We investigate both numerically and analytically the spectrum evolution of a novel type soliton - nonlinear chirped accelerating or decelerating soliton - at a femtosecond pulse propagation in a medium containing noble nanoparticles. In our consideration, we take into account one- or two-photon absorption of laser radiation by nanorods, and time-dependent nanorod aspect ratio changing due to their melting or reshaping because of laser energy absorption. The chirped solitons are formed due to the trapping of laser radiation by the nanorods reshaping fronts, if a positive or negative phase-amplitude grating is induced by laser radiation. Accelerating or slowing down chirped soliton formation is accompanied by the soliton spectrum blue or red shift. To prove our numerical results, we derived the approximate analytical law for the spectrum maximum intensity evolution along the propagation coordinate, based on earlier developed approximate analytical solutions for accelerating and decelerating solitons.
Mathematical Theory of Dispersion-Managed Optical Solitons
Biswas, Anjan; Edwards, Matthew
2010-01-01
"Mathematical Theory of Dispersion-Managed Optical Solitons" discusses recent advances covering optical solitons, soliton perturbation, optical cross-talk, Gabitov-Turitsyn Equations, quasi-linear pulses, and higher order Gabitov-Turitsyn Equations. Focusing on a mathematical perspective, the book bridges the gap between concepts in engineering and mathematics, and gives an outlook to many new topics for further research. The book is intended for researchers and graduate students in applied mathematics, physics and engineering and also it will be of interest to those who are conducting research in nonlinear fiber optics. Dr. Anjan Biswas is an Associate Professor at the Department of Applied Mathematics & Theoretical Physics, Delaware State University, Dover, DE, USA; Dr. Daniela Milovic is an Associate Professor at the Department of Telecommunications, Faculty of Electronic Engineering, University of Nis, Serbia; Dr. Matthew Edwards is the Dean of the School of Arts and Sciences at Alabama A & M Univ...
Is DNA a nonlinear dynamical system where solitary conformational ...
Indian Academy of Sciences (India)
Unknown
DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The ... nonlinear differential equations and their soliton-like solu- .... structure and dynamics can be added till the most accurate.
Limits to compression with cascaded quadratic soliton compressors
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw
2008-01-01
We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong....... This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find......, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account....
The ion-acoustic soliton: A gas-dynamic viewpoint
International Nuclear Information System (INIS)
McKenzie, J.F.
2002-01-01
The properties of fully nonlinear ion-acoustic solitons are investigated by interpreting conservation of total momentum as the structure equation for the proton flow in the wave. In most studies momentum conservation is regarded as the first integral of the Poisson equation for the electric potential and is interpreted as being analogous to a particle moving in a pseudo-potential well. By adopting an essentially gas-dynamic viewpoint, which emphasizes momentum conservation and the properties of the Bernoulli-type energy equations, the crucial role played by the proton sonic point becomes apparent. The relationship (implied by energy conservation) between the electron and proton speeds in the transition yields a locus--the hodograph of the system-which shows that, in the first half of the soliton, the electrons initially lag behind the protons until the charge neutral point is reached, after which they run ahead of the protons. The system reaches an equilibrium point (the center of the soliton) before the proton flow goes sonic. It follows that the critical ion-acoustic Mach number, M c , above which smooth, continuous solitons cannot be constructed, stems from the requirement that the two equilibrium points of the structure equation coalesce at the proton sonic point of the flow. In general the range of the ion-acoustic Mach numbers, M ep , in which solitons exist, is extended beyond the classical range 1 ep 2 shaped pulses characteristic of weakly nonlinear waves and shows that solitons exist only if 1 ep e and 10kT e depending upon the values of the adiabatic indices of the electrons and protons and the proton Mach number
Zhong, Rong-Xuan; Huang, Nan; Li, Huang-Wu; He, He-Xiang; Lü, Jian-Tao; Huang, Chun-Qing; Chen, Zhao-Pin
2018-04-01
We numerically and analytically investigate the formations and features of two-dimensional discrete Bose-Einstein condensate solitons, which are constructed by quadrupole-quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.
Soliton microcomb range measurement
Suh, Myoung-Gyun; Vahala, Kerry J.
2018-02-01
Laser-based range measurement systems are important in many application areas, including autonomous vehicles, robotics, manufacturing, formation flying of satellites, and basic science. Coherent laser ranging systems using dual-frequency combs provide an unprecedented combination of long range, high precision, and fast update rate. We report dual-comb distance measurement using chip-based soliton microcombs. A single pump laser was used to generate dual-frequency combs within a single microresonator as counterpropagating solitons. We demonstrated time-of-flight measurement with 200-nanometer precision at an averaging time of 500 milliseconds within a range ambiguity of 16 millimeters. Measurements at distances up to 25 meters with much lower precision were also performed. Our chip-based source is an important step toward miniature dual-comb laser ranging systems that are suitable for photonic integration.
Cubic-quintic solitons in the checkerboard potential
International Nuclear Information System (INIS)
Driben, Rodislav; Zyss, Joseph; Malomed, Boris A.; Gubeskys, Arthur
2007-01-01
We introduce a two-dimensional (2D) model which combines a checkerboard potential, alias the Kronig-Penney (KP) lattice, with the self-focusing cubic and self-defocusing quintic nonlinear terms. The beam-splitting mechanism and soliton multistability are explored in this setting, following the recently considered 1D version of the model. Families of single- and multi-peak solitons (in particular, five- and nine-peak species naturally emerge in the 2D setting) are found in the semi-infinite gap, with both branches of bistable families being robust against perturbations. For single-peak solitons, the variational approximation (VA) is developed, providing for a qualitatively correct description of the transition from monostability to the bistability. 2D solitons found in finite band gaps are unstable. Also constructed are two different species of stable vortex solitons, arranged as four-peak patterns ('oblique' and 'straight' ones). Unlike them, compact 'crater-shaped' vortices are unstable, transforming themselves into randomly walking fundamental beams
Properties of one-dimensional anharmonic lattice solitons
Szeftel, Jacob; Laurent-Gengoux, Pascal; Ilisca, Ernest; Hebbache, Mohamed
2000-12-01
The existence of bell- and kink-shaped solitons moving at constant velocity while keeping a permanent profile is studied in infinite periodic monoatomic chains of arbitrary anharmonicity by taking advantage of the equation of motion being integrable with respect to solitons. A second-order, non-linear differential equation involving advanced and retarded terms must be solved, which is done by implementing a scheme based on the finite element and Newton's methods. If the potential has a harmonic limit, the asymptotic time-decay behaves exponentially and there is a dispersion relation between propagation velocity and decay time. Inversely if the potential has no harmonic limit, the asymptotic regime shows up either as a power-law or faster than exponential. Excellent agreement is achieved with Toda's model. Illustrative examples are also given for the Fermi-Pasta-Ulam and sine-Gordon potentials. Owing to integrability an effective one-body potential is worked out in each case. Lattice and continuum solitons differ markedly from one another as regards the amplitude versus propagation velocity relationship and the asymptotic time behavior. The relevance of the linear stability analysis when applied to solitons propagating in an infinite crystal is questioned. The reasons preventing solitons from arising in a diatomic lattice are discussed.
Soliton filtering from a supercontinuum: a tunable femtosecond pulse source
Energy Technology Data Exchange (ETDEWEB)
Licea-Rodriguez, Jacob; Rangel-Rojo, Raul [Centro de Investigacion CientIfica y de Educacion Superior de Ensenada, Apartado Postal 2732, Ensenada B.C., 22860 (Mexico); Garay-Palmett, Karina, E-mail: rrangel@cicese.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico DF. 04510 (Mexico)
2011-01-01
In this article we report experimental results related with the generation of a supercontinuum in a microstructured fiber, from which the soliton with the longest wavelength is filtered out of the continuum and is used to construct a tunable ultrashort pulses source by varying the pump power. Pulses of an 80 fs duration (FWHM) from a Ti:sapphire oscillator were input into a 2 m long fiber to generate the continuum. The duration of the solitons at the fiber output was preserved by using a zero dispersion filtering system, which selected the longest wavelength soliton, while avoiding temporal spreading of the solitons. We present a complete characterization of the filtered pulses that are continuously tunable in the 850-1100 nm range. We also show that the experimental results have a qualitative agreement with theory. An important property of the proposed near-infrared pulsed source is that the soliton pulse energies obtained after filtering are large enough for applications in nonlinear microscopy.
Head-on collisions of electrostatic solitons in multi-ion plasmas
International Nuclear Information System (INIS)
Verheest, Frank; Hellberg, Manfred A.; Hereman, Willy A.
2012-01-01
Head-on collisions between two electrostatic solitons are dealt with by the Poincaré-Lighthill-Kuo method of strained coordinates, for a plasma composed of a number of cold (positive and negative) ion species and Boltzmann electrons. The nonlinear evolution equations for both solitons and their phase shift due to the collision, resulting in time delays, are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is special enough to replace the quadratic by a cubic nonlinearity in the evolution equations, with concomitant repercussions on the phase shifts. Applications include different two-ion plasmas, showing positive or negative polarity solitons in the generic case. At critical composition, a combination of a positive and a negative polarity soliton is possible.
Oscillations in the interactions among multiple solitons in an optical fibre
Energy Technology Data Exchange (ETDEWEB)
Hu, Wen-Qiang; Gao, Yi-Tian; Zhao, Chen; Feng, Yu-Jie; Su, Chuan-Qi [Beijing University of Aeronautics and Astronautics (China). Ministry of Education Key Laboratory of Fluid Mechanics; Beijing University of Aeronautics and Astronautics (China). National Laboratory for Computational Fluid Dynamics
2016-07-01
In this article, under the investigation on the interactions among multiple solitons for an eighth-order nonlinear Schroedinger equation in an optical fibre, oscillations in the interaction zones are observed theoretically. With different coefficients of the operators in this equation, we find that (1) the oscillations in the solitonic interaction zones have different forms with different spectral parameters of this equation; (2) the oscillations in the interactions among the multiple solitons are affected by the choice of spectral parameters, the dispersive effects and nonlinearity of the eighth-order operator; (3) the second-, fifth-, sixth-, and seventh-order operators restrain oscillations in the solitonic interaction zones and the higher-order operators have stronger attenuated effects than the lower ones, while the third- and fourth-order operators stimulate and extend the scope of oscillations.
Stability of Modified K-dV soliton in plasma with negative ion
International Nuclear Information System (INIS)
Matsukawa, Michiaki; Watanabe, Shinsuke
1988-01-01
The K-P and Modified K-P equations for ion acoustic wave are derived from the fluid equations for plasma with negative ion. At the critical density of the negative ion where the nonlinearity of the K-P equation vanishes, the ion acoustic soliton is described by the Modified K-P equation. The stability of Modified K-dV soliton against bending are investigated by using the Modified K-P equation. It is found that the soliton is stable, independent of the sign of amplitude. (author)
Self-generation and management of spin-electromagnetic wave solitons and chaos
International Nuclear Information System (INIS)
Ustinov, Alexey B.; Kondrashov, Alexandr V.; Nikitin, Andrey A.; Kalinikos, Boris A.
2014-01-01
Self-generation of microwave spin-electromagnetic wave envelope solitons and chaos has been observed and studied. For the investigation, we used a feedback active ring oscillator based on artificial multiferroic, which served as a nonlinear waveguide. We show that by increasing the wave amplification in the feedback ring circuit, a transition from monochromatic auto-generation to soliton train waveform and then to dynamical chaos occurs in accordance with the Ruelle-Takens scenario. Management of spin-electromagnetic-wave solitons and chaos parameters by both dielectric permittivity and magnetic permeability of the multiferroic waveguiding structure is demonstrated.
Time-reversal focusing of an expanding soliton gas in disordered replicas
Fratalocchi, Andrea
2011-05-31
We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time-reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schrödinger equation.
Time-reversal focusing of an expanding soliton gas in disordered replicas
Fratalocchi, Andrea; Armaroli, A.; Trillo, S.
2011-01-01
We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time-reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schrödinger equation.
Spontaneous soliton formation and modulational instability in Bose-Einstein condensates
International Nuclear Information System (INIS)
Carr, L.D.; Brand, J.
2004-01-01
The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [K. E. Strecker et al., Nature (London) 417, 150 (2002).] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton-soliton interactions, produces bursts of hot atoms at different time scales
The Neutrosophic Logic View to Schrodinger's Cat Paradox, Revisited
Directory of Open Access Journals (Sweden)
Florentin Smarandache
2008-07-01
Full Text Available The present article discusses Neutrosophic logic view to Schrodinger's cat paradox. We argue that this paradox involves some degree of indeterminacy (unknown which Neutrosophic logic can take into consideration, whereas other methods including Fuzzy logic cannot. To make this proposition clear, we revisit our previous paper by offering an illustration using modified coin tossing problem, known as Parrondo's game.
Torsional Newton-Cartan geometry and the Schrodinger algebra
Bergshoeff, Eric A.; Hartong, Jelle; Rosseel, Jan
2015-01-01
We show that by gauging the Schrodinger algebra with critical exponent z and imposing suitable curvature constraints, that make diffeomorphisms equivalent to time and space translations, one obtains a geometric structure known as (twistless) torsional Newton-Cartan geometry (TTNC). This is a version
Boundary triples for Schrodinger operators with singular interactions on hypersurfaces
Czech Academy of Sciences Publication Activity Database
Behrndt, J.; Langer, M.; Lotoreichik, Vladimir
2016-01-01
Roč. 7, č. 2 (2016), s. 290-302 ISSN 2220-8054 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : boundary triple * Weyl function * Schrodinger operator * singular potential * delta-interaction * hypersurface Subject RIV: BE - Theoretical Physics
Orbital stability of Gausson solutions to logarithmic Schrodinger equations
Directory of Open Access Journals (Sweden)
Alex H. Ardila
2016-12-01
Full Text Available In this article we prove of the orbital stability of the ground state for logarithmic Schrodinger equation in any dimension and under nonradial perturbations. This general stability result was announced by Cazenave and Lions [9, Remark II.3], but no details were given there.
A model for the stochastic origins of Schrodinger's equation
Davidson, Mark P.
2001-01-01
A model for the motion of a charged particle in the vacuum is presented which, although purely classical in concept, yields Schrodinger's equation as a solution. It suggests that the origins of the peculiar and nonclassical features of quantum mechanics are actually inherent in a statistical description of the radiative reactive force.
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym
2007-01-01
In this paper, we study a system of coupled nonlinear Schroedinger equations modelling a quantum degenerate mixture of bosons and fermions. We analyze the stability of plane waves, give precise conditions for the existence of solitons and write explicit solutions in the form of periodic waves. We also check that the solitons observed previously in numerical simulations of the model correspond exactly to our explicit solutions and see how plane waves destabilize to form periodic waves
Analogies between dark solitons in atomic Bose-Einstein condensates and optical systems
International Nuclear Information System (INIS)
Proukakis, N P; Parker, N G; Frantzeskakis, D J; Adams, C S
2004-01-01
Dark solitons have been observed in optical systems (optical fibres, dielectric guides and bulk media), and, more recently, in harmonically confined atomic Bose-Einstein condensates. This paper presents an overview of some of the common features and analogies experienced by these two intrinsically nonlinear systems, with emphasis on the stability of dark solitons in such systems and their decay via emission of radiation. The closely related issue of vortex dynamics in such systems is also briefly discussed
A perturbation method for dark solitons based on a complete set of the squared Jost solutions
International Nuclear Information System (INIS)
Ao Shengmei; Yan Jiaren
2005-01-01
A perturbation method for dark solitons is developed, which is based on the construction and the rigorous proof of the complete set of squared Jost solutions. The general procedure solving the adiabatic solution of perturbed nonlinear Schroedinger + equation, the time-evolution equation of dark soliton parameters and a formula for calculating the first-order correction are given. The method can also overcome the difficulties resulting from the non-vanishing boundary condition