Compression limits in cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw
2008-01-01
Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency.......Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency....
Cascaded Quadratic Soliton Compression in Waveguide Structures
DEFF Research Database (Denmark)
Guo, Hairun
to further push such multi-cycle pulses into few-cycle and even single-cycle. In this thesis, we investigate the high order soliton compression in quadratic nonlinear waveguide structures, which is a one-step pulse compression scheme making use of the soliton regime -- with the spontaneous cancelation...... and self-defocusing Kerr effect so that the soliton is created and the soliton self-compression happens in the normal dispersion region. Meanwhile, the chromatic dispersion in the waveguide is also tunable, understood as the dispersion engineering with structural designs. Therefore, compared to commonly...... used two-step compression scheme with e.g. hollow-core photonic crystal fibers plus a dispersion compensation component, our scheme, called the cascaded quadratic soliton compression (CQSC), provides a simpler setup with larger tunability on the nonlinearity, and could avoid the problem with the self...
Critical Boundary of Cascaded Quadratic Soliton Compression in PPLN
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2012-01-01
Cascaded quadratic soliton compression in PPLN is investigated and a general critical soliton number is found as the compression boundary. An optimal-parameter diagram for compression at 1550 nm is presented.......Cascaded quadratic soliton compression in PPLN is investigated and a general critical soliton number is found as the compression boundary. An optimal-parameter diagram for compression at 1550 nm is presented....
Cascaded quadratic soliton compression at 800 nm
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey
2007-01-01
We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion.......We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
Experiments on Cascaded Quadratic Soliton Compression in Unpoled LN Waveguide
DEFF Research Database (Denmark)
Guo, Hairun; Zhou, Binbin; Zeng, Xianglong
2014-01-01
Experiments on cascaded quadratic soliton compression in unpoled phasemismatched lithium niobate waveguides are presented. Pulse self-phasemodulation dominated by an overall self-defocusing nonlinearity is observed, with an variation of pump wavelength and waveguide core width. © 2014 Optical...
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...
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)]....
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....
Soliton compression to few-cycle pulses by cascaded quadratic nonlinearities
DEFF Research Database (Denmark)
Bache, Morten; Moses, Jeffrey; Bang, Ole
2007-01-01
Theoretical and numerical investigation of pulse-compression in a nonlinear crystal is presented. SHG soliton number is introduced and show that compression only takes place when it is larger than the "usual" Kerr soliton number. Pulse compression with cascaded quadratic nonlinearities requires...... that the ratio of the SHG and Kerr soliton numbers N>1....
DEFF Research Database (Denmark)
Bache, Morten; Moses, Jeffrey; Wise, Frank W.
2008-01-01
The output of a high-power femtosecond fiber laser is typically 300 fs with a wavelength around $\\lambda=1030-1060$ nm. Our numerical simulations show that cascaded quadratic soliton compression in bulk LiNbO$_3$ can compress such pulses to below 100 fs.......The output of a high-power femtosecond fiber laser is typically 300 fs with a wavelength around $\\lambda=1030-1060$ nm. Our numerical simulations show that cascaded quadratic soliton compression in bulk LiNbO$_3$ can compress such pulses to below 100 fs....
Quadratic solitons as nonlocal solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole
2003-01-01
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...... solutions and the prediction of bound states of quadratic solitons....
DEFF Research Database (Denmark)
Bache, Morten; Lægsgaard, Jesper; Bang, Ole
2007-01-01
We investigate the possibility of using poled silica photonic crystal fibers for self-defocusing soliton compression with cascaded quadratic nonlinearities. Such a configuration has promise due to the desirable possibility of reducing the group-velocity mismatch. However, this unfortunately leads...... to increased phase mismatch, and the dispersion is often anomalous. All this reduces the design parameter space where soliton compression is possible, and poses strong requirements on the poling efficiency. We propose to use quasi-phase matching in order to reach realistic requirements on the quadratic...
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...
DEFF Research Database (Denmark)
Bache, Morten; Wise, Frank W.
2010-01-01
The output pulses of a commercial high-power femtosecond fiber laser or amplifier are typically around 300–500 fs with wavelengths of approximately 1030 nm and tens of microjoules of pulse energy. Here, we present a numerical study of cascaded quadratic soliton compression of such pulses in LiNbO3...
Zeng, Xianglong; Guo, Hairun; Zhou, Binbin; Bache, Morten
2012-11-19
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. Numerical results show that compressed pulses with less than three-cycle duration can be achieved even when the compression factor is very large, and in contrast to standard soliton compression, these compressed pulses have minimal pedestal and high quality factor.
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...
DEFF Research Database (Denmark)
Bache, Morten
2009-01-01
The dispersion of index-guiding microstructured polymer optical fibers is calculated for second-harmonic generation. The quadratic nonlinearity is assumed to come from poling of the polymer, which in this study is chosen to be the cyclic olefin copolymer Topas. We found a very large phase mismatch...
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...
Dynamics of soliton cascades in fiber amplifiers.
Arteaga-Sierra, F R; Antikainen, A; Agrawal, Govind P
2016-11-15
We study numerically the formation of cascading solitons when femtosecond optical pulses are launched into a fiber amplifier with less energy than required to form a soliton of equal duration. As the pulse is amplified, cascaded fundamental solitons are created at different distances, without soliton fission, as each fundamental soliton moves outside the gain bandwidth through the Raman-induced spectral shifts. As a result, each input pulse creates multiple, temporally separated, ultrashort pulses of different wavelengths at the amplifier output. The number of pulses depends not only on the total gain of the amplifier but also on the width of the input pulse.
Spatiotemporal solitons in quadratic nonlinear media
Indian Academy of Sciences (India)
Optical solitons are localized electromagnetic waves that propagate stably in nonlinear me- dia with group-velocity dispersion (GVD) and/or diffraction. Temporal solitons in single- mode optical fibers are the prototypical optical solitons; these were predicted theoretically in 1973 [1] and first observed experimentally in 1980 ...
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...
Cascaded Soliton Compression of Energetic Femtosecond Pulses at 1030 nm
DEFF Research Database (Denmark)
Bache, Morten; Zhou, Binbin
2012-01-01
We discuss soliton compression with cascaded second-harmonic generation of energetic femtosecond pulses at 1030 nm. We discuss problems encountered with soliton compression of long pulses and show that sub-10 fs compressed pulses can be achieved.......We discuss soliton compression with cascaded second-harmonic generation of energetic femtosecond pulses at 1030 nm. We discuss problems encountered with soliton compression of long pulses and show that sub-10 fs compressed pulses can be achieved....
Cascadable spatial-soliton logic gates.
Blair, S; Wagner, K
2000-11-10
The three-terminal spatial-soliton angular-deflection geometry provides the characteristics of an inverting logic gate with gain, and phase-insensitive implementations can be realized by a number of specific nonlinear interactions between orthogonally polarized waves. In particular, numerical simulations of spatial-soliton dragging and collision are used to calculate the transfer functions of inverter and multiple configurations of two-input nor gates and to address their cascadability. These transfer functions converge in cascaded operation and suggest that fan-out greater than 2 with a large noise margin is attainable in a system with standardized signal levels. These results are obtained with the material properties of fused silica and are representative of low-loss Kerr media.
DEFF Research Database (Denmark)
Esbensen, B.K.; Bache, Morten; Krolikowski, W.
2012-01-01
We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description...... this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions....
Stable solitons of quadratic ginzburg-landau equations
Crasovan; Malomed; Mihalache; Mazilu; Lederer
2000-07-01
We present a physical model based on coupled Ginzburg-Landau equations that supports stable temporal solitary-wave pulses. The system consists of two parallel-coupled cores, one having a quadratic nonlinearity, the other one being effectively linear. The former core is active, with bandwidth-limited amplification built into it, while the latter core has only losses. Parameters of the model can be easily selected so that the zero background is stable. The model has nongeneric exact analytical solutions in the form of solitary pulses ("dissipative solitons"). Direct numerical simulations, using these exact solutions as initial configurations, show that they are unstable; however, the evolution initiated by the exact unstable solitons ends up with nontrivial stable localized pulses, which are very robust attractors. Direct simulations also demonstrate that the presence of group-velocity mismatch (walkoff) between the two harmonics in the active core makes the pulses move at a constant velocity, but does not destabilize them.
Cascaded photonic crystal fibers for three-stage soliton compression.
Li, Qian; Cheng, Zihao
2016-11-01
Cascaded higher-order soliton compression in photonic crystal fibers (PCFs) is demonstrated, where both the hyperbolic secant and Gaussian input pulses are considered. Detailed fiber designs for three-stage higher-order soliton compression where soliton order is three or non-integer are presented. A highest compression factor of 221.32 has been achieved with only 49.48% pedestal energy.
Coalescence cascade of dissipative solitons in parametrically driven systems
Clerc, M. G.; Coulibaly, S.; Gordillo, L.; Mujica, N.; Navarro, R.
2011-09-01
Parametrically driven spatially extended systems exhibit uniform oscillations which are modulationally unstable. The resulting periodic state evolves to the creation of a gas of dissipative solitons. Driven by the interaction of dissipative solitons, the multisoliton state undergoes a cascade of coalescence processes, where the average soliton separation distance obeys a temporal self-similar law. Starting from the soliton pair interaction law, we have derived analytically and characterized the law of this multisoliton coarsening process. A comparison of numerical results obtained with different models such as the parametrically driven damped nonlinear Schrödinger equation, a vertically driven chain of pendula, and a parametrically forced magnetic wire, shows remarkable agreement. Both phenomena, the pair interaction law and the coarsening process, are also observed experimentally in a quasi-one-dimensional layer of Newtonian fluid which is oscillated vertically.
DEFF Research Database (Denmark)
Bache, Morten; Moses, Jeffrey; Lægsgaard, Jesper
2007-01-01
We show theoretically that high-quality soliton compression from ~500 fs to ~10 fs is possible in poled silica photonic crystal fibers using cascaded (2):(2) nonlinearities. A moderate group-velocity mismatch optimizes the compression....
Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Bang, Ole; Kivshar, Yu.S.
1997-01-01
We show that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic (or chi((2))) medium is strongly influenced by induced Kerr effects, such as self- and cross-phase modulation. We prove the existence of rapidly oscillating solitary waves (a spatial analog of the g...... of the guided-center soliton) supported by the quadratic and induced cubic nonlinearities....
DEFF Research Database (Denmark)
Zeng, Xianglong; Guo, Hairun; Zhou, Binbin
2012-01-01
In few-cycle soliton generation with large compression factors using cascaded nonlinearities the pulse quality can be improved by engineering quasi-phase-matching structures. The soliton-induced mid-IR optical Cherenkov wave is also enhanced.......In few-cycle soliton generation with large compression factors using cascaded nonlinearities the pulse quality can be improved by engineering quasi-phase-matching structures. The soliton-induced mid-IR optical Cherenkov wave is also enhanced....
DEFF Research Database (Denmark)
Wang, Shaofei; Guo, Hairun; Fan, Dengfeng
2013-01-01
The cascaded soliton spectral tunneling (SST) effect is proposed and numerically investigated in multiple optical fiber segments, which work together to transfer the soliton pulse over a wide wavelength span. A triple-cladding fiber and a solid core step-index photonic crystal fiber are carefully...... be flexible tuned by tailoring the position of ZDWs. Numerical simulations in both fiber segments are shown, and a soliton transfer over 570 nm is demonstrated with two fiber segments. Meanwhile, soliton pulse compression and supercontinuum generation are also observed to accompany each SST effect....
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.
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...
Zhang, Lifu; Liu, Kun; Zhong, Haizhe; Zhang, Jinggui; Deng, Jianqin; Li, Ying; Fan, Dianyuan
2015-07-15
Soliton propagation direction can be engineered in optical fibers in the presence of high-order effects (HOEs). It is well known that Raman effects can decelerate the soliton. Here we investigate the manipulation of the deceleration or acceleration of soliton emitted from Airy pulse whose spectrum is imposed an initial quadratic phase modulation (QPM) in optical fibers in the absence of HOEs. We show that, under the action of the anomalous second-order dispersion (SOD) and Kerr nonlinearity, Airy pulse with QPM is able to emit soliton with acceleration or deceleration depending on whether the QPM is negative or positive, and at a rate that is determined by the magnitude of QPM. The reason is that the acceleration behaviors of incident Airy pulse is altered depending on whether SOD and QPM have the same or opposite signs. Our study shows the possibility of controlling and manipulating the soliton propagation and interaction in optical fibers without HOEs, by purposely choosing appropriate QPM parameter of an Airy pulse.
DEFF Research Database (Denmark)
Liu, Xing; Zhou, Binbin; Guo, Hairun
2015-01-01
We show numerically that ultrashort self-defocusing temporal solitons colliding with a weak pulsed probe in the near-IR can convert the probe to the mid-IR. A near-perfect conversion efficiency is possible for a high effective soliton order. The near-IR self-defocusing soliton can form in a quadr...
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
DEFF Research Database (Denmark)
Zhou, Binbin; Bache, Morten; Chong, A.
2010-01-01
By launching energetic femtosecond pulses in a lithium niobate crystal, the phase mismatched second-harmonic generation process compresses the 50 fs input pulse at 1250 nm to 30 fs through a soliton effect.......By launching energetic femtosecond pulses in a lithium niobate crystal, the phase mismatched second-harmonic generation process compresses the 50 fs input pulse at 1250 nm to 30 fs through a soliton effect....
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....
Few-cycle nonlinear mid-IR pulse generated with cascaded quadratic nonlinearities
DEFF Research Database (Denmark)
Bache, Morten; Liu, Xing; Zhou, Binbin
Generating few-cycle energetic and broadband mid-IR pulses is an urgent current challenge in nonlinear optics. Cascaded second-harmonic generation (SHG) gives access to an ultrafast and octave-spanning self-defocusing nonlinearity: when ΔkL >> 2π the pump experiences a Kerr-like nonlinear index...
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...
Quasiperiodic Envelope Solitons
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Kivshar, Yuri S.; Bang, Ole
1999-01-01
We analyze nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics. the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point...... out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally....
Driben, Rodislav; Mitschke, Fedor; Zhavoronkov, Nickolai
2010-12-06
The complex mechanism of multiple interactions between solitary and dispersive waves at the advanced stage of supercontinuum generation in photonic crystal fiber is studied in experiment and numerical simulations. Injection of high power negatively chirped pulses near zero dispersion frequency results in an effective soliton fission process with multiple interactions between red shifted Raman solitons and dispersive waves. These interactions may result in relative acceleration of solitons with further collisions between them of quasi-elastic or quasi-plastic kinds. In the spectral domain these processes result in enhancement of certain wavelength regions within the spectrum or development of a new significant band at the long wavelength side of the spectrum.
Multi-wavelength and multi-colour temporal and spatial optical solitons
DEFF Research Database (Denmark)
Kivshar, Y. S.; Sukhorukov, A. A.; Ostrovskaya, E. A.
2000-01-01
We present an overview of several novel types of multi- component envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high performance computer networks, mult......-color parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons in Fibonacci optical superlattices....
Generation of multicolor spatial solitons with pulsed light
Carrasco Rodríguez, Sílvia; Pérez Torres, Juan; Artigas García, David; Torner Sabata, Lluís
2001-01-01
The impact of temporal effects to the generation of multiple wave quadratic spatial solitons with pulsed light is shown. We examine soliton formation under conditions of second-harmonic generation but our conclusions are relevant to soliton formation in all parametric processes. It is shown how group-velocity mismatch between the multiple interacting signals prevents spatial soliton formation with too short pulses. Illustrative examples of the minimum pulse width allowed for soliton generatio...
Salerno, Mario; Quintero, Niurka R.
2001-01-01
The mechanism underlying the soliton ratchet, both in absence and in presence of noise, is investigated. We show the existence of an asymmetric internal mode on the soliton profile that couples, through the damping in the system, to the soliton translational mode. Effective soliton transport is achieved when the internal mode and the external force are phase locked. We use as a working model a generalized double sine-Gordon equation. The phenomenon is expected to be valid for generic soliton ...
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)
Asymmetric spatial soliton dragging.
Blair, S; Wagner, K; McLeod, R
1994-12-01
A new low-latency, cascadable optical logic gate with gain, high contrast, and three-terminal input-output isolation is introduced. The interaction between two orthogonally polarized spatial solitons brought into coincidence at the boundary of a saturating nonlinear medium and propagating in different directions results in the phase-insensitive spatial dragging of a strong pump soliton by a weaker signal. As a result, the strong pump is transmitted through an aperture when the weak signal is not present, and it is dragged to the side by more than a beam width and blocked in the presence of the weak signal, thus implementing an inverter with gain. A multi-input, logically complete NOR gate also can be implemented in a cascaded system.
Fay, Temple H.
2012-01-01
Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…
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...
Rosenberger, Tessa; Lindner, John F.
We study the dynamics of mechanical arrays of bistable elements coupled one-way by wind. Unlike earlier hydromechanical unidirectional arrays, our aeromechanical one-way arrays are simpler, easier to study, and exhibit a broader range of phenomena. Soliton-like waves propagate in one direction at speeds proportional to wind speeds. Periodic boundaries enable solitons to annihilate in pairs in even arrays where adjacent elements are attracted to opposite stable states. Solitons propagate indefinitely in odd arrays where pairing is frustrated. Large noise spontaneously creates soliton- antisoliton pairs, as predicted by prior computer simulations. Soliton annihilation times increase quadratically with initial separations, as expected for random walk models of soliton collisions.
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
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
Controllable nonlocal behaviour by cascaded second-harmonic generation of fs pulses
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw
2008-01-01
Second-harmonic generation (SHG) of ultra-short pulses can act as a prototypical nonlocal nonlinear model, since the strength and nature of the temporal nonlocality can be controlled through the phase-mismatch parameter. The presence of a group-velocity mismatch namely implies that when the phase...... mismatch is small the nonlocal response function becomes oscillatory, while for large phase mismatch it becomes localized. In the transition between the two regimes the strength of the nonlocality diverges, and the system goes from a weakly nonlocal to a strongly nonlocal state. When simulating soliton...... compression to few-cycle pulses in the cascaded quadratic soliton compressor, the spectral content of the full coupled SHG model is predicted by the nonlocal model even when few-cycle pulses are interacting....
Zhang, Xiaoen; Chen, Yong
2017-11-01
In this paper, a combination of stripe soliton and lump soliton is discussed to a reduced (3+1)-dimensional Jimbo-Miwa equation, in which such solution gives rise to two different excitation phenomena: fusion and fission. Particularly, a new combination of positive quadratic functions and hyperbolic functions is considered, and then a novel nonlinear phenomenon is explored. Via this method, a pair of resonance kink stripe solitons and rogue wave is studied. Rogue wave is triggered by the interaction between lump soliton and a pair of resonance kink stripe solitons. It is exciting that rogue wave must be attached to the stripe solitons from its appearing to disappearing. The whole progress is completely symmetry, the rogue wave starts itself from one stripe soliton and lose itself in another stripe soliton. The dynamic properties of the interaction between one stripe soliton and lump soliton, rogue wave are discussed by choosing appropriate parameters.
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)
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.
DEFF Research Database (Denmark)
Zhou, Binbin; Bache, Morten
2016-01-01
Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystals like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband...... supercontinuum generation in the visible, near-IR, and short-wavelength mid-IR. Here we conduct an experiment where a mid-IR crystal is pumped in the mid-IR. The crystal is cut for noncritical interaction, so the three-wave mixing of a single mid-IR femtosecond pump source leads to highly phase-mismatched second......-harmonic generation. This self-acting cascaded process leads to the formation of a self-defocusing soliton at the mid-IR pump wavelength and after the self-compression point multiple octave-spanning supercontinua are observed. The results were recorded in a commercially available crystal LiInS2 pumped in the 3-4 µm...
Induced Kerr effects and self-guided beams in quasi-phase-matched quadratic media [CBC4
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Bang, Ole; Kivshar, Yuri S.
1997-01-01
We show that quasi-phase-matching of quadratic media induces Kerr effects, such as self- and cross-phase modulation, and leads to the existence of a novel class of solitary waves, QPM-solitons......We show that quasi-phase-matching of quadratic media induces Kerr effects, such as self- and cross-phase modulation, and leads to the existence of a novel class of solitary waves, QPM-solitons...
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
Topological Solitons in Physics.
Parsa, Zohreh
1979-01-01
A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)
Chiu, Hong-Yee
1990-01-01
The theory of Lee and Pang (1987), who obtained solutions for soliton stars composed of zero-temperature fermions and bosons, is applied here to quark soliton stars. Model soliton stars based on a simple physical model of the proton are computed, and the properties of the solitons are discussed, including the important problem of the existence of a limiting mass and thus the possible formation of black holes of primordial origin. It is shown that there is a definite mass limit for ponderable soliton stars, so that during cooling a soliton star might reach a stage beyond which no equilibrium configuration exists and the soliton star probably will collapse to become a black hole. The radiation of ponderable soliton stars may alter the short-wavelength character of the cosmic background radiation, and may be observed as highly redshifted objects at z of about 100,000.
Petnikova, V. M.; Shuvalov, Vladimir V.
2009-07-01
The domains of existence and peculiarities of exact analytic solutions of the problem of quasi-synchronous interaction of four plane collinear monochromatic waves — modes in a quadratically nonlinear medium during cascade frequency conversion are analysed. It is shown that the unusual types of multicomponent cnoidal and solitary soliton-like waves (of periodic and aperiodic energy-exchange regimes) are realised. Two of the four components of the latter are proportional to the real and imaginary parts of the well-known Lorentzian dependence, which is commonly used to describe the dispersion of contributions from resonance transitions to the complex permittivity in the case of homogeneous line broadening.
Indian Academy of Sciences (India)
Abstract. As an introduction to the special issue on nonlinear waves, solitons and their signiﬁcance in physics are reviewed. The soliton is the ﬁrst universal concept in nonlinear science. Universality and ubiquity of the soliton concept are emphasized.
Dispersive waves in fs cascaded second-harmonic generation
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw
2009-01-01
Dispersive waves are observed in simulations of cascaded (phase-mismatched) second-harmonic generation. When generating ultra-short fs compressed near-IR solitons the dispersive waves are strongly red-shifted, depending on the soliton wavelength. Semi-analytical calculations predict the wavelengths....
Luo, Rui; Liang, Hanxiao; Lin, Qiang
2016-07-25
We show a new class of complex solitary wave that exists in a nonlinear optical cavity with appropriate dispersion characteristics. The cavity soliton consists of multiple soliton-like spectro-temporal components that exhibit distinctive colors but coincide in time and share a common phase, formed together via strong inter-soliton four-wave mixing and Cherenkov radiation. The multicolor cavity soliton shows intriguing spectral locking characteristics and remarkable capability of spectrum management to tailor soliton frequencies, which would be very useful for versatile generation and manipulation of multi-octave spanning phase-locked Kerr frequency combs, with great potential for applications in frequency metrology, optical frequency synthesis, and spectroscopy.
Indian Academy of Sciences (India)
V. Suresh University Of Hyderabad Hyderabad
2008-10-31
Oct 31, 2008 ... Historically, the study of quadratic forms was part of number theory; Minkowski, Siegel, Hasse, Eichler, Kneser and several other mathematicians created a rich arithmetic theory of quadratic forms. V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic forms ...
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…
Bednyakova, Anastasia; Turitsyn, Sergei K
2015-03-20
The key to generating stable optical pulses is mastery of nonlinear light dynamics in laser resonators. Modern techniques to control the buildup of laser pulses are based on nonlinear science and include classical solitons, dissipative solitons, parabolic pulses (similaritons) and various modifications and blending of these methods. Fiber lasers offer remarkable opportunities to apply one-dimensional nonlinear science models for the design and optimization of very practical laser systems. Here, we propose a new concept of a laser based on the adiabatic amplification of a soliton pulse in the cavity-the adiabatic soliton laser. The adiabatic change of the soliton parameters during evolution in the resonator relaxes the restriction on the pulse energy inherent in traditional soliton lasers. Theoretical analysis is confirmed by extensive numerical modeling.
Blanco-Redondo, Andrea; Martijn, de Sterke C.; Sipe, J.E.; Krauss, Thomas F.; Eggleton, Benjamin J.; Husko, Chad
2016-01-01
Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of anomalous group-velocity dispersion and self-phase modulation. Here we experimentally demonstrate a class of bright soliton arising purely from the interaction of negative fourth-order dispersion and self-phase modulation, which can occur even for normal group-velocity dispersion. We provide experimental and numerical evidence of shape-preserving propagation and flat temporal phase for the fundamental pure-quartic soliton and periodically modulated propagation for the higher-order pure-quartic solitons. We derive the approximate shape of the fundamental pure-quartic soliton and discover that is surprisingly Gaussian, exhibiting excellent agreement with our experimental observations. Our discovery, enabled by precise dispersion engineering, could find applications in communications, frequency combs and ultrafast lasers. PMID:26822758
Solitonic Josephson Thermal Transport
Guarcello, Claudio; Solinas, Paolo; Braggio, Alessandro; Giazotto, Francesco
2018-03-01
We explore the coherent thermal transport sustained by solitons through a long Josephson junction as a thermal gradient across the system is established. We observe that a soliton causes the heat current through the system to increase. Correspondingly, the junction warms up in conjunction with the soliton, with temperature peaks up to, e.g., approximately 56 mK for a realistic Nb-based proposed setup at a bath temperature Tbath=4.2 K . The thermal effects on the dynamics of the soliton are also discussed. Markedly, this system inherits the topological robustness of the solitons. In view of these results, the proposed device can effectively find an application as a superconducting thermal router in which the thermal transport can be locally mastered through solitonic excitations, whose positions can be externally controlled through a magnetic field and a bias current.
Chiu, Hong-Yee
1990-01-01
The structure of nontopological solutions of Einstein field equations as proposed by Friedberg, Lee, and Pang (1987) is examined. This analysis incorporates finite temperature effects and pair creation. Quarks are assumed to be the only species that exist in interior of soliton stars. The possibility of primordial creation of soliton stars in the incomplete decay of the degenerate vacuum in early universe is explored. Because of dominance of pair creation inside soliton stars, the luminosity of soliton stars is not determined by its radiative transfer characteristics, and the surface temperature of soliton stars can be the same as its interior temperature. It is possible that soliton stars are intense X-ray radiators at large distances. Soliton stars are nearly 100 percent efficient energy converters, converting the rest energy of baryons entering the interior into radiation. It is possible that a sizable number of baryons may also be trapped inside soliton stars during early epochs of the universe. In addition, if soliton stars exist they could assume the role played by massive black holes in galactic centers.
Gravitation and quadratic forms
Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha
2017-03-01
The light-cone Hamiltonians describing both pure ( N = 0) Yang-Mills and N = 4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N = 8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
Gravitation and quadratic forms
Energy Technology Data Exchange (ETDEWEB)
Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)
2017-03-31
The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
International Nuclear Information System (INIS)
San Martin, Jesus; Rodriguez-Perez, Daniel
2009-01-01
Presented in this work are some results relative to sequences found in the logistic equation bifurcation diagram, which is the unimodal quadratic map prototype. All of the different saddle-node bifurcation cascades, associated with every last appearance p-periodic orbit (p=3,4,5,...), can also be generated from the very Feigenbaum cascade. In this way it is evidenced the relationship between both cascades. The orbits of every saddle-node bifurcation cascade, mentioned above, are located in different chaotic bands, and this determines a sequence of orbits converging to every band-merging Misiurewicz point. In turn, these accumulation points form a sequence whose accumulation point is the Myrberg-Feigenbaum point. It is also proven that the first appearance orbits in the n-chaotic band converge to the same point as the last appearance orbits of the (n + 1)-chaotic band. The symbolic sequences of band-merging Misiurewicz points are computed for any window.
Yaşar, Emrullah; Yıldırım, Yakup; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Triki, Houria; Biswas, Anjan; Belic, Milivoj
2017-11-01
This paper obtains optical soliton solution to perturbed nonlinear Schrödinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.
Lump Solutions and Resonance Stripe Solitons to the (2+1-Dimensional Sawada-Kotera Equation
Directory of Open Access Journals (Sweden)
Xian Li
2017-01-01
Full Text Available Based on the symbolic computation, a class of lump solutions to the (2+1-dimensional Sawada-Kotera (2DSK equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 74; Issue 6. Compactons versus solitons ... by their amplitude. Consequently, these models admit soliton solutions in addition to compactons and are integrable. ... Centre for Mathematical Science, City University London, Northampton Square, London EC1V 0HB, UK ...
Semirelativity and Kink Solitons
Nowak, Mariusz Karol
2014-01-01
It is hard to observe relativistic effects in everyday life. However, table experiments using a mechanical transmission line for solitons may be an efficient and simple way to show effects such as Lorentz contraction in a classroom. A kink soliton is a deformation of a lattice of several dozen or more pendulums placed on a wire and connected by a…
Indian Academy of Sciences (India)
generalized Korteweg–de Vries equations admit genuine soliton solutions besides com- pacton solitary waves. For models which admit stable compactons having a width which is independent of their amplitude and those which possess unstable compacton solutions the Painlevé test fails, such that no soliton solutions can ...
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2014-01-01
Self-defocusing soliton compression supported by the cascaded phase-mismatched second-harmonic generation process is numerically demonstrated in unpoled lithium niobate ridge waveguides where nano-joule pulses are operated and quasi-phase-matching is unnecessary. The soliton range is 1100-1800 nm....
A revisit to quadratic programming with fuzzy parameters
International Nuclear Information System (INIS)
Liu, S.-T.
2009-01-01
Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.
Elliptic Quadratic Operator Equations
Ganikhodjaev, Rasul; Mukhamedov, Farrukh; Saburov, Mansoor
2017-01-01
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method is also presented for stable solutions.
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.
Dickmann, M
2015-01-01
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in
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.
Ellis, John; Sueiro, Maria
2014-01-01
Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.
Separable quadratic stochastic operators
International Nuclear Information System (INIS)
Rozikov, U.A.; Nazir, S.
2009-04-01
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Wyller, John
2004-01-01
We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons....
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
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 87; Issue 5. Breaking soliton ... We use the simplified Hirota's method to obtain multiple soliton solutions for each developed breaking soliton equation. We also develop ... WAZWAZ1. Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA ...
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models.We establish the distinctdispersion relation for each equation. We use the simplified Hirota's method to obtain multiple soliton ...
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Abstract. Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable- coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota's bilinear method. The bilinear forms and analytic soliton solutions are derived, and the ...
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.
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.
Noncommuting Momenta of Topological Solitons
Watanabe, Haruki; Murayama, Hitoshi
2014-05-01
We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.
Nonlinear compression of optical solitons
Indian Academy of Sciences (India)
pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects. Keywords. Optical solitons; bright and dark solitons; nonlinear compression; phase modulation; fibre amplification; loss. PACS Nos 42.81. Dp; 02.30 Jr; 04.30 Nk. 1. Introduction. The term soliton refers to special kinds of waves that ...
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.
Quadratic Malcev superalgebras
Albuquerque, Helena; Benayadi, Saı̈d
2004-01-01
A quadratic Malcev superalgebra is a Malcev superalgebra with a non-degenerate supersymmetric even invariant bilinear form B; B is called an invariant scalar product on M. In this paper, we obtain the inductive classifications of quadratic Malcev algebras and of Malcev superalgebras such that is a reductive Malcev algebra and the action of the on is completely reducible. http://www.sciencedirect.com/science/article/B6V0K-49KST23-1/1/76b688f435c1b5f20f8bd222655704cb
Soliton Perturbations, Revisited.
Herman, Russell Leland
Starting with an 'integrable' nonlinear evolution equation, we are investigating perturbations about a one soliton solution, through the inversion of a linear equation for the first order correction. This differs from the methods based on the perturbation of certain 'scattering data', as the proposed method takes place in coordinate space, and not spectral space. The method is tested on several perturbed Korteweg -DeVries equations. The damped KdV equation is studied in detail, resulting in the resolution of the controversy over the shift in the center of the soliton in favor of the results of Karpman and Maslov. Using a finite difference scheme, a numerically induced shift in the damped soliton's position is predicted through the use of perturbation theory. We extend the results of Ott and Sudan for other damped KdV equations, giving expressions for the shift in soliton position and the asymptotic form of the first order correction to the solution. Next we investigate Menyuk's case of a solution consisting of a soliton plus arbitrary initial radiation, which is subject to a Hamiltonian perturbation; and we show that the radiation must start out small. After these preliminary investigations, we turn to the stochastic KdV equation with external Gaussian white noise, zeta(x,t). For the cases of damping and no damping, the averaged soliton asymptotically becomes a Gaussian wave packet, which decays and broadens according to the same power laws as found by Wadati and Akutsu for the noise zeta(t). Next, we investigate the propagation of a modulated KP soliton and compare our results to the work of Chang. We find that singular perturbation theory cannot explain the evolution of this profile, but we can obtain good qualitative results from the solution of the Cauchy problem for the linearized KP equation. The modulations travel away from the soliton peak and decay in time, leaving a stable planar soliton behind. Finally, we discuss the application of the method to the
International Nuclear Information System (INIS)
Hause, A.; Mitschke, F.
2010-01-01
Two solitons in an optical fiber can form pairs in which the double-humped shape is maintained even when the pair is shifted in frequency by the Raman effect. We show here analytically that this is possible even when the two solitons have unequal power. We discuss the forces that cause relative motion of the two solitons, and determine a condition for balance, i.e., for a pair to maintain their separation while the phase keeps evolving. At a specific parameter point we find a solution in which even the phase profile of the pulse pair is maintained. We then discuss that this special point exists also for multipeak structures, or soliton trains. These trains can move as an entity due to Raman shifting. The results are tested by numerical simulation. A comparison to literature reveals that both the rotating phase pair and the constant phase soliton pair apparently have been seen before by others in numerical simulations. Our treatment provides the general framework.
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.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2016-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
Bonilla, L L; Carretero, M; Terragni, F; Birnir, B
2016-08-09
Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but it may also be induced by tumours to amplify their own growth. Mathematical and computational models contribute to understanding angiogenesis and developing anti-angiogenic drugs, but most work only involves numerical simulations and analysis has lagged. A recent stochastic model of tumour-induced angiogenesis including blood vessel branching, elongation, and anastomosis captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density. Here we find that the latter advances chemotactically towards the tumour driven by a soliton (similar to the famous Korteweg-de Vries soliton) whose shape and velocity change slowly. Analysing these collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process.
Klasifikasi Interaksi Gelombang Permukaan Bertipe Dua Soliton
sutimin, Sutimin; Rusgiyono, Agus
2001-01-01
Pada tulisan ini diselidiki, masalah klasifikasi interaksi gelombang bertipe dua soliton Kadomtsev-Petviashvilli (KP). Disini dianalisis berdasarkan parameter interaksi dua solusi soliton baik melalui harga eksak maupun proses pelimitan. Proses pelimitan ini dilakukan untuk mengetahui resonansi diantara dua soliton. Selanjutnya resonansi soliton ini dikaji untuk mendapatkan soliton yang baru.
Soliton equations solved by the boundary CFT
Saito, Satoru; Sato, Ryuichi
2003-01-01
Soliton equations are derived which characterize the boundary CFT a la Callan et al. Soliton fields of classical soliton equations are shown to appear as a neutral bound state of a pair of soliton fields of BCFT. One soliton amplitude under the influence of the boundary is calculated explicitly and is shown that it is frozen at the Dirichlet limit.
Direct soliton generation in microresonators.
Bao, Chengying; Xuan, Yi; Jaramillo-Villegas, Jose A; Leaird, Daniel E; Qi, Minghao; Weiner, Andrew M
2017-07-01
We investigate, numerically and experimentally, the effect of thermo-optical (TO) chaos on soliton generation dynamics in microresonators. Numerical simulations that include the thermal dynamics show that the generated solitons can either survive or annihilate when the pump laser is scanned from blue to red and then stop at a fixed wavelength; the outcome is stochastic and is strongly related to the number of solitons generated. The random fluctuations of the cavity resonance occurring under TO chaos are also found to trigger delayed spontaneous soliton generation after the laser scan ends, which could enable soliton excitation with slow laser tuning speed. Stochastic soliton annihilation/survival, as well as delayed spontaneous soliton generation, is observed experimentally in a silicon-nitride microresonator.
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.
Obregon, Maria; Raj, Nawin; Stepanyants, Yury
2018-03-01
The adiabatic decay of different types of internal wave solitons caused by the Earth's rotation is studied within the framework of the Gardner-Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions: (ut + c ux + α u ux + α1 u2 ux + β uxxx)x = γ u. It is shown that at the early stage of evolution solitons gradually decay under the influence of weak Earth's rotation described by the parameter γ. The characteristic decay time is derived for different types of solitons for positive and negative coefficients of cubic nonlinearity α1 (both signs of that parameter may occur in the oceans). The coefficient of quadratic nonlinearity α determines only a polarity of solitary wave when α1 0. It is found that the adiabatic theory describes well the decay of solitons having bell-shaped profiles. In contrast to that, large amplitude table-top solitons, which can exist when α1 is negative, are structurally unstable. Under the influence of Earth's rotation, they transfer first to the bell-shaped solitons, which decay then adiabatically. Estimates of the characteristic decay time of internal solitons are presented for the real oceanographic conditions.
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
National Research Council Canada - National Science Library
Rebbi, Claudio; Soliani, G
1984-01-01
... may find in the reprints on the mathematical theories of solitons useful ideas and inspirations, while the latter may find in this volume interesting and challenging applications of the concept of solitons in the domain of particle physics. We would like to express our gratitude to the many colleagues, in particular to Sidney Coleman, Neil Craigie, Roman Jackiw and Ed Witten, who have given us advice in the selection of the reprints. We are also thankful to Dr. Phua and World Scientific Publishing Co. for giving u...
Hidden conic quadratic representation of some nonconvex quadratic optimization problems
Ben-Tal, A.; den Hertog, D.
The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general......., and algorithms are developed on a case by case basis. There lacks an analytical representation of a general or even a convex quadratic spline. The current paper fills this gap by providing an analytical representation of a general quadratic spline. Furthermore, for convex quadratic spline, it is shown...
Self-trapped optical beams: Spatial solitons
Indian Academy of Sciences (India)
We present a brief overview of the basic concepts of the theory ofspatial optical solitons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary waves in nonintegrable nonlinear models.
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Indian Academy of Sciences (India)
The Painlevé test is passed for models allowing for compacton solutions whose width is determined by their amplitude. Consequently, these models admit soliton solutions in ... Compactons; PT -symmetry; KdV equation; Painlevé test. .... Cooper et al [25] found that in the generalized KdV equation, i.e. m = 2, a necessary.
Indian Academy of Sciences (India)
For models which admit stable compactons having a width which is independent of their amplitude and those which possess unstable compacton solutions the Painlevé test fails, such that no soliton solutions can be found. The Painlevé test is passed for models allowing for compacton solutions whose width is determined ...
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
Semiclassical geons as solitonic black hole remnants
Energy Technology Data Exchange (ETDEWEB)
Lobo, Francisco S.N. [Centro de Astronomia e Astrofísica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisboa (Portugal); Olmo, Gonzalo J.; Rubiera-Garcia, D., E-mail: flobo@cii.fc.ul.pt, E-mail: gonzalo.olmo@csic.es, E-mail: drubiera@fisica.ufpb.br2 [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia - CSIC. Universidad de Valencia, Burjassot-46100, Valencia (Spain)
2013-07-01
We find that the end state of black hole evaporation could be represented by non-singular and without event horizon stable solitonic remnants with masses of the order the Planck scale and up to ∼ 16 units of charge. Though these objects are locally indistinguishable from spherically symmetric, massive electric (or magnetic) charges, they turn out to be sourceless geons containing a wormhole generated by the electromagnetic field. Our results are obtained by interpreting semiclassical corrections to Einstein's theory in the first-order (Palatini) formalism, which yields second-order equations and avoids the instabilities of the usual (metric) formulation of quadratic gravity. We also discuss the potential relevance of these solutions for primordial black holes and the dark matter problem.
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
Interaction of spatial photorefractive solitons
DEFF Research Database (Denmark)
Królikowski, W.; Denz, C.; Stepken, A.
1998-01-01
We present a review of our recent theoretical and experimental results on the interaction of two-dimensional solitary beams in photorefractive SBN crystals. We show that the collision of coherent solitons may result in energy exchange, fusion of the interacting solitons, the birth of a new solita...... that a soliton pair may experience both attractive and repulsive forces; depending on their mutual separation. We also show that strong attraction leads to periodic collision or helical motion of solitons depending on initial conditions.......We present a review of our recent theoretical and experimental results on the interaction of two-dimensional solitary beams in photorefractive SBN crystals. We show that the collision of coherent solitons may result in energy exchange, fusion of the interacting solitons, the birth of a new solitary...
Soliton stability criterion for generalized nonlinear Schrödinger equations.
Quintero, Niurka R; Mertens, Franz G; Bishop, A R
2015-01-01
A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that p'(v)0 is a necessary condition for stability; here, v is the soliton velocity and p=P/N, where P and N are the soliton momentum and norm, respectively. To date, the curve p(v) was calculated approximately by a collective coordinate theory, and the criterion was confirmed by simulations. The goal of this paper is to calculate p(v) exactly for several classes and cases of the generalized NLSE: a soliton moving in a real potential, in particular a time-dependent ramp potential, and a time-dependent confining quadratic potential, where the nonlinearity in the NLSE also has a time-dependent coefficient. Moreover, we investigate a logarithmic and a cubic NLSE with a time-independent quadratic potential well. In the latter case, there is a bisoliton solution that consists of two solitons with asymmetric shapes, forming a bound state in which the shapes and the separation distance oscillate. Finally, we consider a cubic NLSE with parametric driving. In all cases, the p(v) curve is calculated either analytically or numerically, and the stability criterion is confirmed.
Directory of Open Access Journals (Sweden)
C. Adam
2016-03-01
Full Text Available 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.
Chiral solitons a review volume
1987-01-01
This review volume on topological and nontopological chiral solitons presents a global view on the current developments of this field in particle and nuclear physics. The book addresses problems in quantization, restoration of translational and rotational symmetry, and the field theoretical approach to solitons which are common problems in the field of solitons. Primarily aimed for graduate students and the novice in the field, the collected articless cover a broad spectrum of topics in formalism as well as phenomenology.
Biological soliton in multicellular movement
Kuwayama, Hidekazu; Ishida, Shuji
2013-01-01
Solitons have been observed in various physical phenomena. Here, we show that the distinct characteristics of solitons are present in the mass cell movement of non-chemotactic mutants of the cellular slime mould Dictyostelium discoideum. During starvation, D. discoideum forms multicellular structures that differentiate into spore or stalk cells and, eventually, a fruiting body. Non-chemotactic mutant cells do not form multicellular structures; however, they do undergo mass cell movement in the form of a pulsatile soliton-like structure (SLS). We also found that SLS induction is mediated by adhesive cell-cell interactions. These observations provide novel insights into the mechanisms of biological solitons in multicellular movement. PMID:23893301
Scale symmetry of quantum solitons
International Nuclear Information System (INIS)
Chepilko, N.M.; Fujii, K.; Kobushkin, A.P.
1991-01-01
A collective-coordinate Lagrangian for a rotating and vibrating quantum soliton in the nonlinear σ-model is shown to possess a symmetry under scale transformation of the chiral field. Using this symmetry an integrodifferential equation for the chiral angle is obtained. A consistency condition between this equation and the Schroedinger equation for the quantum soliton is also discussed. At limiting cases (a vibrating, but not rotating soliton; or a rotating, but not vibrating soliton) the integrodifferential ones and the chiral angle becomes independent of the solution of the Schroedinger equation. 7 refs
Exact periodic and solitonic states of the spinor condensates in a uniform external potential
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhi-Hai [School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051 (China); Yang, Shi-Jie, E-mail: yangshijie@tsinghua.org.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2016-08-15
We propose a method to analytically solve the one-dimensional coupled nonlinear Gross–Pitaevskii equations which govern the motion of the spinor Bose–Einstein condensates. In a uniform external potential, several classes of exact periodic and solitonic solutions, either in real or in complex forms, are obtained for both the F=1 and F=2 condensates for the Hamiltonian comprising the kinetic energy, the linear and the quadratic Zeeman energies. Real solutions take the form of composite soliton trains. Complex solutions correspond to the mass counter-flows as well as spin currents. These solutions are general that contains neither approximations nor constraints on the system parameters.
Quadratic ideals, indefinite quadratic forms and some specific diophantine equations
Directory of Open Access Journals (Sweden)
Ahmet Tekcan
2018-07-01
Full Text Available Let $k\\geq 1$ be an integer and let $P=k+2,Q=k$ and $D=k^{2}+4$. In this paper, we derived some algebraic properties of quadratic ideals $I_{\\gamma}$ and indefinite quadratic forms $F_{\\gamma }$ for quadratic irrationals $\\gamma$, and then we determine the set of all integer solutions of the Diophantine equation $F_{\\gamma }^{\\pm k}(x,y=\\pm Q$.
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
2016-10-06
Oct 6, 2016 ... as optical fibres, fluid dynamics, plasma physics, ocean engineering, chemical physics etc. are described by nonlinear equations where soliton solutions may appear. Some of these nonlinear evolution equations are integrable which give multiple soliton solutions. The study of integrable equations, that ...
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
2016-10-06
Oct 6, 2016 ... Abstract. We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models. We establish the distinct dispersion relation for each equation. We use the simplified Hirota's method to ...
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.
Gravitational field of Schwarzschild soliton
Directory of Open Access Journals (Sweden)
Musavvir Ali
2015-01-01
Full Text Available The aim of this paper is to study the gravitational field of Schwarzschild soliton. Use of characteristic of λ-tensor is given to determine the kinds of gravitational fields. Through the cases of two and three dimension for Schwarzschild soliton, the Gaussian curvature is expressed in terms of eigen values of the characteristic equation.
Breather soliton dynamics in microresonators
Yu, Mengjie; Jang, Jae K.; Okawachi, Yoshitomo; Griffith, Austin G.; Luke, Kevin; Miller, Steven A.; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L.
2017-01-01
The generation of temporal cavity solitons in microresonators results in coherent low-noise optical frequency combs that are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems, manifesting themselves as a localized temporal structure that exhibits oscillatory behaviour. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation. Our study constitutes a significant contribution to understanding the soliton dynamics within the larger context of nonlinear science. PMID:28232720
Soliton mobility in disordered lattices.
Sun, Zhi-Yuan; Fishman, Shmuel; Soffer, Avy
2015-10-01
We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model and the standard nonlinear Schrödinger (NLS) lattice with the help of an effective potential generalizing the Peierls-Nabarro potential. This potential results from a deviation from integrability, which is due to randomness for the AL model, and both randomness and lattice discreteness for the NLS lattice. The statistical properties of such a potential are analyzed, and it is shown how the soliton mobility is affected by its size. The usefulness of this effective potential in studying soliton dynamics is demonstrated numerically. Furthermore, we propose two ways to enhance soliton transport in the presence of disorder: one is to use specific realizations of randomness, and the other is to consider a specific soliton pair.
Binary classification posed as a quadratically constrained quadratic ...
Indian Academy of Sciences (India)
Particle swarm optimization (PSO) is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The central idea is to use PSO to move in the direction towards optimal solution rather than searching the entire ...
Binary classification posed as a quadratically constrained quadratic ...
Indian Academy of Sciences (India)
DEEPAK KUMAR
Abstract. Particle swarm optimization (PSO) is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The cen- tral idea is to use PSO to move in the direction towards optimal solution rather than searching the entire ...
Solitons and quasi-periodic behaviors in an inhomogeneous optical fiber
Yang, Jin-Wei; Gao, Yi-Tian; Su, Chuan-Qi; Zuo, Da-Wei; Feng, Yu-Jie
2017-01-01
In this paper, a fifth-order variable-coefficient nonlinear Schrödinger equation for the attosecond pulses in an inhomogeneous optical fiber is studied. With the aid of auxiliary functions, we obtain the variable-coefficient Hirota bilinear equations and corresponding integrable constraints. Under those constraints, we obtain the Lax pair, conservation laws, one-, two- and three-soliton solutions via the Hirota method and symbolic computation. Soliton structures and interactions are discussed: (1) For the one soliton, we discuss the influence of the group velocity dispersion term α(x) and fifth-order dispersion term δ(x) on the velocities and structures of the solitons, where x is the normalized propagation along the fiber, and derive a constraint contributing to the stationary soliton; (2) For the two solitons, we analyze the interactions between them with different values of α(x) and δ(x), and derive the quasi-periodic formulae for three cases of the bound states: When α(x) and δ(x) are the linear functions of x, quasi-periodic attraction and repulsion lead to the redistribution of the energy of the two solitons, and ratios among the quasi-periods are derived; When α(x) and δ(x) are the quadratic functions of x, the ratios among them are also obtained; When α(x) and δ(x) are the periodic functions of x, bi-periodic phenomena are obtained; (3) For the three solitons, including the parabolic, cubic, periodic and stationary structures, interactions among them with different values of the α(x) and δ(x) are presented.
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
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...... is parametrically tunable over 1000 nm by changing the three-wave mixing phase-matching condition. The results are important for the bright and broadband supercontinuum generation and for the frequency comb generation in quadratic nonlinear microresonators....
Parametrically Tunable Soliton-Induced Resonant Radiation by Three-Wave Mixing.
Zhou, B B; Liu, X; Guo, H R; Zeng, X L; Chen, X F; Chung, H P; Chen, Y H; Bache, M
2017-04-07
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 phase-matching 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 is parametrically tunable over 1000 nm by changing the three-wave mixing phase-matching condition. The results are important for the bright and broadband supercontinuum generation and for the frequency comb generation in quadratic nonlinear microresonators.
Carroll, RW
1991-01-01
When soliton theory, based on water waves, plasmas, fiber optics etc., was developing in the 1960-1970 era it seemed that perhaps KdV (and a few other equations) were really rather special in the set of all interesting partial differential equations. As it turns out, although integrable systems are still special, the mathematical interaction of integrable systems theory with virtually all branches of mathematics (and with many currently developing areas of theoretical physics) illustrates the importance of this area. This book concentrates on developing the theme of the tau function. KdV and K
Soliton equations and pseudospherical surfaces
International Nuclear Information System (INIS)
Sasaki, R.
1979-03-01
All the soliton equations in 1+1 dimensions that can be solved by the AKNS 2x2 inverse scattering method (for example, the sine-Gordon, KdV or Modified KdV equations) are shown to describe pseudospherical surfaces, i.e. surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws, and Baecklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out. (Auth.)
Basic methods of soliton theory
Cherednik, I
1996-01-01
In the 25 years of its existence Soliton Theory has drastically expanded our understanding of "integrability" and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local cons
International Nuclear Information System (INIS)
Rajaraman, R.
1982-01-01
In recent years, a host of new non-perturbative results in relativistic quantum field theory have been obtained, based on classical soliton and instanton solutions. This book offers an elementary and unified introduction to these developments. Such solutions are derived for a variety of models and classified by topological indices. The methods are then developed for quantizing solitons to obtain quantum particles. Vacuum tunnelling, theta-vacua and the dilute-instanton-gas approximation are described in detail. Other instanton effects related to quark-quark forces, confinement, the U(1) problem and Borel summability are also discussed. The emphasis is on presenting the basic ideas in a simple pedagogical way. Technical tools like functional methods, Grassman integrals, homotopy classification, collective coordinates etc. are developed from the very outset. The presentation of this work is kept at a fairly simple level, and ideas are developed through illustrative examples. Techniques not covered in older field theory textbooks, such as functional integral methods, are presented in some detail to the necessary extent. These techniques are important in their own right. The book is mainly addressed to particle physicists and quantum field theorists. (Auth.)
Solitons in relativistic cosmologies
International Nuclear Information System (INIS)
Pullin, J.
1988-08-01
The application to the construction of solitonic cosmologies in General Relativity of the Inverse Scattering Technique of Belinskii an Zakharov is analyzed. Three improvements to the mentioned technique are proposed: the inclusion of higher order poles in the scattering matrix, a new renormalization technique for diagonal metrics and the extension of the technique to include backgrounds with material content by means of a Kaluza-Klein formalism. As a consequence of these improvements, three new aspects can be analyzed: a) The construction of anisotropic and inhomogeneous cosmological models which can mimic the formation of halos and voids, due to the presence of a material content. The new renormalization technique allows to construct an exact perturbation theory. b) The analysis of the dynamics of models with cosmological constant (inflationary models) and their perturbations. c) The study of interaction of gravitational solitonic waves on material backgrounds. Moreover, some additional works, connected with the existance of 'Crack of doom' type singularities in Kaluza-Klein cosmologies, stochastic perturbations in inflationary universes and inflationary phase transitions in rotating universes are described. (Author) [es
Giesemann, Jens; Greiner, Martin; Lipa, Peter
1997-02-01
The generators of binary multiplicative cascade models with a non-overlapping branching structure are given by the Haar wavelets. We construct specific generalizations of these models for which any given wavelet represents the generators of the local cascade branchings. Such “wavelet cascades”, for which we calculate spatial correlation functions, have spatially overlapping branches and are therefore useful for modeling recombination effects in hierarchical branching processes.
A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions
International Nuclear Information System (INIS)
Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan
2007-01-01
In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported
International Nuclear Information System (INIS)
Fujioka, J.; Espinosa C, A.; Rodriguez, R.F.
2006-01-01
At the end of the nineties a brand-new type of soliton was discovered: the embedded solitons. Initially they were found in optical systems, and afterwards they were also found in hydrodynamic models, liquid crystal theory and discrete systems. These peculiar solitary waves are interesting because they exist under conditions in which, until recently, the propagation ol solitons was thought to be impossible. At first these nonlinear waves were believed to be necessarily isolated and unstable, but later on it was found that they can be stable and may exist in families. This paper explains what these embedded solitons are, in which models they have been found, and what variants exist (stable, unstable, continuous, discrete, etc.) (Author)
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
Energy Technology Data Exchange (ETDEWEB)
Anabalón, Andrés, E-mail: andres.anabalon@uai.cl [Departamento de Ciencias, Facultad de Artes Liberales and Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Astefanesei, Dumitru, E-mail: dumitru.astefanesei@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Choque, David, E-mail: brst1010123@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso (Chile)
2016-11-10
We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate.
All-optical signal processing in quadratic nonlinear materials
DEFF Research Database (Denmark)
Johansen, Steffen Kjær
2002-01-01
and the SH. Via quasi-phase-matching (QPM) the phase mismatch and hence the nonlinearity is eÙectively brought under control through periodic sign reversal of the nonlinearity. On theaverage QPM changes the quadratic nonlinearity and induces new cubic nonlinearities in the system. The engineering...... of materials with a second order nonlinearity, the so-called X(2) materials, is faster and stronger than that of more conventional materials with a cubic nonlinearity. The X(2) materials support spatial solitons consisting of two coupled components, the fundamental wave (FW) and its second harmonic (SH...... are dedicated to this part of the research. In chapter 4 the generality of the theoretical approach is emphasised with the derivation and verification of equivalent tools for media with a saturable nonlinearity. The strength of the X(2) nonlinearity strongly depends on the phase mismatch between the FW...
An Investigation on Quadratic Equations.
Hirst, Keith
1988-01-01
Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)
Cioslowski, Jerzy
2018-04-01
The dependence of the natural amplitudes of the harmonium atom in its ground state on the confinement strength ω is thoroughly investigated. A combination of rigorous analysis and extensive, highly accurate numerical calculations reveals the presence of only one positive-valued natural amplitude ("the normal sign pattern") for all ω ≥1/2 . More importantly, it is shown that unusual, weakly occupied natural orbitals (NOs) corresponding to additional positive-valued natural amplitudes emerge upon sufficient weakening of the confinement. These solitonic NOs, whose shapes remain almost invariant as their radial positions drift toward infinity upon the critical values of ω being approached from below, exhibit strong radial localization. Their asymptotic properties are extracted from the numerical data and their relevance to calculations on fully Coulombic systems is discussed.
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Analytical theory of dark nonlocal solitons
DEFF Research Database (Denmark)
Kong, Qian; Wang, Qi; Bang, Ole
2010-01-01
We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality....
Ultrafast all-optical logic gates based on soliton trapping in fibers.
Islam, M N
1989-11-15
Ultrafast all-optical soliton-trapping logic gates, including an inverter, exclusive OR, and AND, are experimentally demonstrated in birefringent fibers. The soliton-trapping logic gates are three terminal devices with orthogonally polarized inputs, phase-insensitive nonlinear operation, and switching energies of ~42 pJ. Using a 0.2-THz bandpass filter, the contrast ratio for the exclusive-OR gate is ~8:1, but the output pulses are ~10 times broader than the input pulse width. By widening the filter bandpass to 0.58 THz, an inverter is demonstrated with an ~4:1 contrast ratio and output pulses that can propagate as solitons in a fiber. Numerical simulations show that the output from the inverter can be cascaded to other trapping gates.
Scaling properties of pure-quartic solitons
DEFF Research Database (Denmark)
Blanco-Redondo, Andrea; Lo, Chih Wei; Stefani, Alessio
2017-01-01
We demonstrate, by experiments and analytical developments, that the recently discovered pure-quartic solitons significantly outperform conventional solitons for high-energy ultrafast pulses. This is due to the favorable scaling of their energy and their Kelly sidebands.......We demonstrate, by experiments and analytical developments, that the recently discovered pure-quartic solitons significantly outperform conventional solitons for high-energy ultrafast pulses. This is due to the favorable scaling of their energy and their Kelly sidebands....
Two-Dimensional Spatial Solitons in Nematic Liquid Crystals
International Nuclear Information System (INIS)
Zhong Weiping; Xie Ruihua; Goong Chen; Belic, Milivoj; Yang Zhengping
2009-01-01
We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Gaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.
On the supersymmetric solitons and monopoles
International Nuclear Information System (INIS)
Hruby, J.
1978-01-01
The basic results in a new trend in supersymmetry and soliton theory are presented. It is shown that the soliton expectation value of the energy operator is mass of the soliton without the quantum corrections. A new supersymmetric monopole model in three dimensions is constructed by generalization of the supersymmetric sine-Gordon model in one space dimension
Soliton bunching in annular Josephson junctions
DEFF Research Database (Denmark)
Vernik, I.V; Lazarides, Nickos; Sørensen, Mads Peter
1996-01-01
By studying soliton (fluxon) motion in long annular Josephson junctions it is possible to avoid the influence of the boundaries and soliton-soliton collisions present in linear junctions. A new experimental design consisting of a niobium coil placed on top of an annular junction has been used...
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.
Self-trapped optical beams: Spatial solitons
Indian Academy of Sciences (India)
as
tons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary ... suggested as a way to stabilize such a catastrophic self-focusing and produce stable solitary waves of ...... cations of spatial optical solitons towards creating a novel generation of nonlinear optical devices ...
Formation of multiple dark photovoltaic spatial solitons
Indian Academy of Sciences (India)
Photorefractive effect; photovoltaic soliton splitting; multiple dark solitons; beam propagation method. PACS No. 42.65.Jx. 1. Introduction. In the last two decades, photorefractive spatial solitons have attracted much interest due to their potential applications such as all-optical beam switching and routing, optical inter-.
Soliton model for elementary electric charge
International Nuclear Information System (INIS)
Chepilko, N.M.; Kobushkin, A.P.
1988-01-01
The existence and topological stability of three-dimensional solitons in Klein-Gordon field electrodynamics are proved. The central-symmetric solution to field equations, which can be interpreted as soliton model of elementary electric charge with zero spin, is constructed. The electrostatic soliton rotation is shown to result in the charge having its own magnetic-dipole field. 9 refs.; 2 figs
Scattering of waves by Langmuir solitons
Energy Technology Data Exchange (ETDEWEB)
Mendonca, J.T. (Instituto Superior Tecnico, Lisbon (Portugal). Centro de Electrodinamica)
1983-08-01
Scattering of electromagnetic and electrostatic waves by one-dimensional Langmuir solitons in a uniform and isotropic plasma is studied analytically using a perturbation method. Mode conversion via scattering by solitons is also considered. The results are also relevant for the case of ion-acoustic solitons.
Energy Technology Data Exchange (ETDEWEB)
Blyakhman, L.G.; Gromov, E.M.; Onosova, I.V.; Tyutin, V.V., E-mail: vtyutin@hse.ru
2017-05-03
The dynamics of a two-component Davydov–Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg–de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton's component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations. - Highlights: • The dynamics of the Davydov–Scott soliton with initial location or velocity mismatch of the HF component was investigated. • The study was performed within the framework of coupled linear Schrödinger and KdV equations for the HF and LF fields. • Analytical and numerical approaches were used. • The frequency of the DS soliton component oscillation was found. • Stability of the perturbed DS solitons was demonstrated.
Covert, Michael
2015-01-01
This book is intended for software developers, system architects and analysts, big data project managers, and data scientists who wish to deploy big data solutions using the Cascading framework. You must have a basic understanding of the big data paradigm and should be familiar with Java development techniques.
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.
Dabholkar, Atish
This thesis is divided into two chapters. Chapter I is about the dynamics of radiating axionic strings and the lower bound on the mass of the invisible axion. It has been suggested that, without inflation, the decay of axionic strings produced after the Peccei -Quinn phase transition is the primary source of cosmic relic axions. Knowing the density of these axions would then allow the derivation of a cosmological bound on the mass of the axion. In order to obtain a sharp bound it is essential to know the spectrum of the emitted axions and the detailed motion of a global string strongly coupled to the axionic field. To this end, following the analogy with Dirac's treatment of classical radiating electrons, self-consistent renormalized equations are obtained that describe the dynamics of a radiating global string interacting with its surrounding axionic field. The numerical formalism for evolving string trajectories using these equations is described, and is applied to the case of a circular loop. It is argued that for large wavelength oscillations of cosmic string loops, the motion is well approximated by the motion of a free Nambu-Goto string with appropriate renormalization. Consequently, a lower bound of 10 ^{-3} eV on the mass of the axion is obtained. Together with the recent upperbound of 4 times 10^{-4 } eV from the supernova SN1987a, it marginally rules out the invisible axion. Chapter II is about superstrings and solitons. It is shown that the quantum renormalization of the superstring tension vanishes to all orders in string perturbation theory. A low-energy analysis of macroscopic superstrings is presented and various analogies between these superstrings and solitons in supersymmetric theories are discussed. These include the existence of exact multi-string solutions of the low -energy supergravity super-Yang-Mills equations of motion and a Bogomol'nyi bound for the energy per unit length which is saturated by these solutions. Arguments are presented that
Inelastic soliton-soliton interaction in coninin models
International Nuclear Information System (INIS)
Simonov, Yu.A.; Veselov, A.I.
1980-01-01
The field equations with nonlinearity proportional to |PSI|sup(-α)PSI, α>0 (model 1 of Simonov-Tjon) are solved in one spatial dimension with initial conditions corresponding to two colliding solitons. One or several breathers are generated during the collision process and the solitons remain stable after collision. An extensive study is done of the collision process and the breather generation for different values of the interaction parameter α, velocities and relative phase in the initial state. In addition the collision of two breathers is considered. Some comparative study of one dimensional model of the Werle type is also done
Students' understanding of quadratic equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
Solitonic fullerene structures in light atomic nuclei.
Battye, R A; Sutcliffe, P M
2001-04-30
The Skyrme model is a classical field theory which has topological soliton solutions. These solitons are candidates for describing nuclei, with an identification between the numbers of solitons and nucleons. We have computed numerically, using two different minimization algorithms, minimum energy configurations for up to 22 solitons. We find, remarkably, that the solutions for seven or more solitons have nucleon density isosurfaces in the form of polyhedra made of hexagons and pentagons. Precisely these structures arise, though at the much larger molecular scale, in the chemistry of carbon shells, where they are known as fullerenes.
Smoothing quadratic and cubic splines
Oukropcová, Kateřina
2014-01-01
Title: Smoothing quadratic and cubic splines Author: Kateřina Oukropcová Department: Department of Numerical Mathematics Supervisor: RNDr. Václav Kučera, Ph.D., Department of Numerical Mathematics Abstract: The aim of this bachelor thesis is to study the topic of smoothing quadratic and cubic splines on uniform partitions. First, we define the basic con- cepts in the field of splines, next we introduce interpolating splines with a focus on their minimizing properties for odd degree and quadra...
Stability in quadratic torsion theories
Energy Technology Data Exchange (ETDEWEB)
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2017-11-15
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
Stability in quadratic torsion theories
Vasilev, Teodor Borislavov; Cembranos, Jose A. R.; Valcarcel, Jorge Gigante; Martín-Moruno, Prado
2017-11-01
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier.
Towards visible soliton microcomb generation.
Lee, Seung Hoon; Oh, Dong Yoon; Yang, Qi-Fan; Shen, Boqiang; Wang, Heming; Yang, Ki Youl; Lai, Yu-Hung; Yi, Xu; Li, Xinbai; Vahala, Kerry
2017-11-03
Frequency combs have applications that extend from the ultra-violet into the mid-infrared bands. Microcombs, a miniature and often semiconductor-chip-based device, can potentially access most of these applications, but are currently more limited in spectral reach. Here, we demonstrate mode-locked silica microcombs with emission near the edge of the visible spectrum. By using both geometrical and mode-hybridization dispersion control, devices are engineered for soliton generation while also maintaining optical Q factors as high as 80 million. Electronics-bandwidth-compatible (20 GHz) soliton mode locking is achieved with low pumping powers (parametric oscillation threshold powers as low as 5.4 mW). These are the shortest wavelength soliton microcombs demonstrated to date and could be used in miniature optical clocks. The results should also extend to visible and potentially ultra-violet bands.
Quark structure of chiral solitons
Energy Technology Data Exchange (ETDEWEB)
Dmitri Diakonov
2004-05-01
There is a prejudice that the chiral soliton model of baryons is something orthogonal to the good old constituent quark models. In fact, it is the opposite: the spontaneous chiral symmetry breaking in strong interactions explains the appearance of massive constituent quarks of small size thus justifying the constituent quark models, in the first place. Chiral symmetry ensures that constituent quarks interact very strongly with the pseudoscalar fields. The ''chiral soliton'' is another word for the chiral field binding constituent quarks. We show how the old SU(6) quark wave functions follow from the ''soliton'', however, with computable relativistic corrections and additional quark-antiquark pairs. We also find the 5-quark wave function of the exotic baryon Theta+.
Scattering in Soliton Models and the Bosonic Exchange description
Coriano', Claudio; Parwani, Rajesh R.; Yamagishi, Hidenaga; Zahed, Ismail
1992-01-01
We argue that the description of meson-nucleon dynamics based on the boson-exchange approach, is compatible with the description of the nucleon as a soliton in the nonrelativistic limit. Our arguments are based on an analysis of the meson-soliton form factor and the exact meson-soliton and soliton-soliton scattering amplitudes in the Sine-Gordon model.
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)
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...... does not exist - one needs to use the nonlocal description, because the nonlocal response function does not converge towards a delta-function. Also, we use the nonlocal theory to show for the first time that the coupling to second harmonic is able to generate an X-shape in the fundamental field despite...
Quadratic prediction of factor scores
Wansbeek, T
1999-01-01
Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic
Stability of Approximate Quadratic Mappings
Directory of Open Access Journals (Sweden)
Kim Hark-Mahn
2010-01-01
Full Text Available We investigate the general solution of the quadratic functional equation , in the class of all functions between quasi- -normed spaces, and then we prove the generalized Hyers-Ulam stability of the equation by using direct method and fixed point method.
Linear Quadratic Games : An Overview
Engwerda, J.C.
2006-01-01
In this paper we review some basic results on linear quadratic differential games.We consider both the cooperative and non-cooperative case.For the non-cooperative game we consider the open-loop and (linear) feedback information structure.Furthermore the effect of adding uncertainty is
On quadratic variation of martingales
Indian Academy of Sciences (India)
starting point for the development of stochastic calculus for continuous semimartingales without bringing in any results from general theory of processes (see [5]). The almost sure convergence of Qn t to 〈M,M〉t also gives a pathwise formula for the quadratic variation of a continuous local martingale. It also directly shows that ...
On quadratic variation of martingales
Indian Academy of Sciences (India)
On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...
Spectral pulse transformations and phase transitions in quadratic nonlinear waveguide arrays.
Setzpfandt, Frank; Sukhorukov, Andrey A; Neshev, Dragomir N; Schiek, Roland; Solntsev, Alexander S; Ricken, Raimund; Min, Yoohong; Sohler, Wolfgang; Kivshar, Yuri S; Pertsch, Thomas
2011-11-07
We study experimentally and numerically the dynamics of a recently found topological phase transition for discrete quadratic solitons with linearly coupled SH waves. We find that, although no stationary states are excited in the experimental situation, the generic feature of the phase transition of the SH is preserved. By utilizing simulations of the coupled mode equations we identify the complex processes leading to the phase transition involving spatial focusing and the generation of new frequency components. These distinct signatures of the dynamic phase transition are also demonstrated experimentally.
Topological and non-topological soliton solutions to some time ...
Indian Academy of Sciences (India)
topological soliton solutions to some time-fractional differential equations. M MIRZAZADEH ... Biswas et al [21,23–27] obtained optical solitons and soliton ..... nonlinear fractional partial differential equations in mathematical and physical sciences.
DEFF Research Database (Denmark)
Olsen, M.; Smith, H.; Scott, Alwyn C.
1984-01-01
A wave tank experiment (first described by the nineteenth-century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment...
Soliton dynamics in directional couplers
Valkering, T.P.; Hoekstra, Hugo; de Boer, Pieter-Tjerk
1998-01-01
The evolution of an initial condition consisting of one soliton(like) pulse in one channel and no signal in the other channel of the coupler is investigated. We focus upon the energy transfer (switching) between the two channels as function of the energy of the signal. For decreasing energy the
Quantum deflation of classical solitons
International Nuclear Information System (INIS)
Sveshnikov, K.; Silaev, P.
1996-01-01
It is shown, that due to nonperturbative effects, in the relativistic QFT the extended particle-like solutions should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytical and numerical results for the dynamics of such a process are given for 1 + 1 dimensional soliton models
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
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.
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Kartashov, Yaroslav V [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain); Egorov, Alexey A [Physics Department, M V Lomonosov Moscow State University, 119899, Moscow (Russian Federation); Vysloukh, Victor A [Departamento de Fisica y Matematicas, Universidad de las Americas-Puebla, Santa Catarina Martir, 72820, Puebla, Cholula (Mexico); Torner, Lluis [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain)
2004-05-01
We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in the appearance of stability (instability) bands in a focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolour periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns.
Inverse problems for difference equations with quadratic ...
African Journals Online (AJOL)
Inverse problems for difference equations with quadratic Eigenparameter dependent boundary conditions. Sonja Currie, Anne D. Love. Abstract. This paper inductively investigates an inverse problem for difference boundary value problems with boundary conditions that depend quadratically on the eigenparameter.
Soliton star in FL-non-topological soliton model and its behavior at high temperature
International Nuclear Information System (INIS)
Xiong Hejin; Li Jiarong
1992-01-01
Based on the FL-non-topological soliton model, the possibility of the formation of the FL-soliton star and its behavior at high temperature are discussed. It is found that the stable, cold and spherical FL-soliton star can be formed, under the necessary condition W > 3B. At high temperature, the FL-soliton bag disappears by the phase transition, but there may be some stellar configuration
Perez-Torres, R.; Belyaeva, T. L.; Hernandez-Tenorio, C.; Kovachev, L. M.; Serkin, V. N.
2010-10-01
The discovery of stimulated Raman self-scattering (SRSS) effect of femtosecond optical solitons is acknowledged to be among the most notable achievements of nonlinear fiber optics. This effect is also often called intrapulse stimulated Raman scattering (ISRS), or soliton self-frequency shift (SSFS), thereby emphasizing the unusual regime of stimulated Raman scattering, when the spectrum of a high-power ultrashort laser pulse proves to be so broad that it covers the band of Raman resonances of the medium. The soliton-like wave packets with continuously shifted spectrum traveling not only in the ordinary space and time, but also in the spectral space, are known as colored femtosecond solitons. Colored solitons play an important role in the soliton supercontinuum generation. The most interesting features of colored optical solitons are connected with the possibility of their tunneling in the spectral domain through a potential barrier-like spectral inhomogeneity of group velocity dispersion (GVD), including the forbidden band of positive GVD. This effect is known as soliton spectral tunneling effect (SST). In this Report, we consider the influence of the soliton binding energy on dynamics of the SST effect assuming that the amplitude and duration of the tunneling soliton vary in time when the soliton spectrum approaches a forbidden GVD barrier. We show that soliton self-compressing effect has dramatic impact on the SST through forbidden spectral region of positive GVD.
KP solitons, total positivity, and cluster algebras
Kodama, Yuji; Williams, Lauren K.
2011-01-01
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili [Kadomtsev BB, Petviashvili VI (1970) Sov Phys Dokl 15:539–541] proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solutions that one obtains in this way come from points of the totally nonnegative part of the Grassmannian. In this paper we explain how the theory of total positivity and cluster algebras provides a framework for understanding these soliton solutions to the KP equation. We then use this framework to give an explicit construction of certain soliton contour graphs and solve the inverse problem for soliton solutions coming from the totally positive part of the Grassmannian. PMID:21562211
Dissipative soliton acceleration in nonlinear optical lattices.
Kominis, Yannis; Papagiannis, Panagiotis; Droulias, Sotiris
2012-07-30
An effective mechanism for dissipative soliton acceleration in nonlinear optical lattices under the presence of linear gain and nonlinear loss is presented. The key idea for soliton acceleration consists of the dynamical reduction of the amplitude of the effective potential experienced by the soliton so that its kinetic energy eventually increases. This is possible through the dependence of the effective potential amplitude on the soliton mass, which can be varied due to the presence of gain and loss mechanisms. In contrast to the case where either the linear or the nonlinear refractive index is spatially modulated, we show that when both indices are modulated with the same period we can have soliton acceleration and mass increasing as well as stable soliton propagation with constant non-oscillating velocity. The acceleration mechanism is shown to be very robust for a wide range of configurations.
On Quadratic Variation of Martingales
Indian Academy of Sciences (India)
where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
Stability of Approximate Quadratic Mappings
Directory of Open Access Journals (Sweden)
Juri Lee
2010-01-01
Full Text Available We investigate the general solution of the quadratic functional equation f(2x+y+3f(2x−y=4f(x−y+12f(x, in the class of all functions between quasi-β-normed spaces, and then we prove the generalized Hyers-Ulam stability of the equation by using direct method and fixed point method.
Geometrical Solutions of Quadratic Equations.
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Extending the Scope of Robust Quadratic Optimization
Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand
In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Zhou, Binbin
2011-01-01
Through cascaded second-harmonic generation, few-cycle solitons can form that resonantly emit strongly red-shifted optical Cherenkov radiation. Numerical simulations show that such dispersive waves can be an efficient source of near- to mid-IR few-cycle broadband pulses.......Through cascaded second-harmonic generation, few-cycle solitons can form that resonantly emit strongly red-shifted optical Cherenkov radiation. Numerical simulations show that such dispersive waves can be an efficient source of near- to mid-IR few-cycle broadband pulses....
Longitudinal soliton tunneling in optical fiber.
Marest, T; Braud, F; Conforti, M; Wabnitz, S; Mussot, A; Kudlinski, A
2017-06-15
We report the observation of the longitudinal soliton tunneling effect in axially varying optical fibers. A fundamental soliton, initially propagating in the anomalous dispersion region of a fiber, can pass through a normal dispersion barrier without being substantially affected. We perform experimental studies by means of spectral and temporal characterizations that show the evidence of the longitudinal soliton tunneling process. Our results are well supported by numerical simulations using the generalized nonlinear Schrödinger equation.
Temperature effects on the Davydov soliton
DEFF Research Database (Denmark)
Cruzeiro, L.; Halding, J.; Christiansen, Peter Leth
1988-01-01
As a possible mechanism for energy storage and transport in proteins, Davydov has proposed soliton formation and propagation. In this paper we investigate the stability of Davydov solitons at biological temperatures. From Davydov’s original theory evolution equations are derived quantum...... mechanically without approximations, and their numerical solutions at different temperatures are presented. Our conclusion is that the Davydov soliton is stable at 310 K....
Soliton-like behavior in fast two-pulse collisions in weakly perturbed linear physical systems
Peleg, Avner; Nguyen, Quan M.; Huynh, Toan T.
2017-12-01
We demonstrate that pulses of linear physical systems, weakly perturbed by nonlinear dissipation, exhibit soliton-like behavior in fast collisions. The behavior is demonstrated for linear waveguides with weak cubic loss and for systems described by linear diffusion-advection models with weak quadratic loss. We show that in both systems, the expressions for the collision-induced amplitude shifts due to the nonlinear loss have the same form as the expression for the amplitude shift in a fast collision between two solitons of the cubic nonlinear Schrödinger equation in the presence of weak cubic loss. Our analytic predictions are confirmed by numerical simulations with the corresponding coupled linear evolution models with weak nonlinear loss. These results open the way for studying dynamics of fast collisions between pulses of weakly perturbed linear physical systems in an arbitrary spatial dimension.
Solitons in one-dimensional antiferromagnetic chains
International Nuclear Information System (INIS)
Pires, A.S.T.; Talim, S.L.; Costa, B.V.
1989-01-01
We study the quantum-statistical mechanics, at low temperatures, of a one-dimensional antiferromagnetic Heisenberg model with two anisotropies. In the weak-coupling limit we determine the temperature dependences of the soliton energy and the soliton density. We have found that the leading correction to the sine-Gordon (SG) expression for the soliton density and the quantum soliton energy comes from the out-of-plane magnon mode, not present in the pure SG model. We also show that when an external magnetic field is applied, the chain supports a new type of kink, where the sublattices rotate in opposite directions
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
Electrical solitons theory, design, and applications
Ricketts, David S
2010-01-01
The dominant medium for soliton propagation in electronics, nonlinear transmission line (NLTL) has found wide application as a testbed for nonlinear dynamics and KdV phenomena as well as for practical applications in ultra-sharp pulse/edge generation and novel nonlinear communication schemes in electronics. While many texts exist covering solitons in general, there is as yet no source that provides a comprehensive treatment of the soliton in the electrical domain.Drawing on the award winning research of Carnegie Mellon's David S. Ricketts, Electrical Solitons Theory, Design, and Applications i
Soliton Gases and Generalized Hydrodynamics
Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien
2018-01-01
We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.
Polarization Properties of Laser Solitons
Directory of Open Access Journals (Sweden)
Pedro Rodriguez
2017-04-01
Full Text Available The objective of this paper is to summarize the results obtained for the state of polarization in the emission of a vertical-cavity surface-emitting laser with frequency-selective feedback added. We start our research with the single soliton; this situation presents two perpendicular main orientations, connected by a hysteresis loop. In addition, we also find the formation of a ring-shaped intensity distribution, the vortex state, that shows two homogeneous states of polarization with very close values to those found in the soliton. For both cases above, the study shows the spatially resolved value of the orientation angle. It is important to also remark the appearance of a non-negligible amount of circular light that gives vectorial character to all the different emissions investigated.
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
Optical solitons in liquid crystals
International Nuclear Information System (INIS)
Yung, Y.S.; Lam, L.
1989-01-01
In this paper, we will discuss theoretically the possible existence of optical solitons in the isotropic liquid and in the nematic phase. For the same compound, when heated, the nematic phase will go through a first order transition at temperature T c to the isotropic liquid phase. As temperature increases from below T c , the orientation order parameter, Q, decreases, drops to zero abruptly at T c and remains zero for T > T c . 10 refs., 1 fig
Factorization method of quadratic template
Kotyrba, Martin
2017-07-01
Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Spatiotemporal soliton clusters in the (3+ 1)-dimensional nonlinear ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 89; Issue 3. Spatiotemporal soliton clusters in the ( 3 + 1 ) -dimensional nonlinear Schrödinger equation with spatially modulated ... Keywords. Nonlinear Schrödinger equation; spatially modulated nonlinearity; Gaussian soliton; vortex soliton; multipole soliton ...
Bergshoeff, Eric A.; Riccioni, Fabio
We construct for arbitrary dimensions a universal T-duality covariant expression for the Wess-Zumino terms of supersymmetric String Solitons in toroidally compactified string theories with 32 supercharges. The worldvolume fields occurring in the effective action of these String Solitons form either
Stable helical solitons in optical media
Indian Academy of Sciences (India)
Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical ﬁbres. We introduce a system of coupled nonlinear Schrödinger equations for the ...
Quantum field theory with soliton conservation laws
Schrör, B
1978-01-01
Field theories with soliton conservation laws are the most promising candidates for explicitly constructable models. The author exemplifies in the case of the massive Thirring model how the old S matrix bootstrap idea, supplemented with a soliton factorization property, may be used as a systematic starting point for the construction of the S matrix, form factors and (hopefully) correlation functions. (34 refs).
Self-trapped optical beams: Spatial solitons
Indian Academy of Sciences (India)
as
Until recently, the theory of spatial optical solitons has been based on the nonlinear. Schrödinger (NLS) equation ... of the theory suggest that many of the properties of optical solitons in non-Kerr media are similar, and they can ...... by A D Boardman, L Pavlov and S Tanev (Kluwer, Dordretch, 1998) pp. 451-475. [7] M Segev ...
Solitons in nonlocal nonlinear media: Exact solutions
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole
2001-01-01
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...... of these solitons and show their stability....
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...
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...
Spatial solitons in nonlinear liquid waveguides
Indian Academy of Sciences (India)
Abstract. Spatial solitons are studied in a planar waveguide filled with nonlinear liquids. Spec- tral and spatial measurements for different geometries and input power of the laser beam show the influence of different nonlinear effects as stimulated scatterings on the soliton propagation and in particular on the beam ...
Gravitational generation of mass in soliton theory
International Nuclear Information System (INIS)
Kozhevnikov, I.R.; Rybakov, Yu.P.
1985-01-01
It is shown that in the framework of a simple scalar field model, that admits soliton solutions, with gravitational field interactions being specially included, one succeeds in ensuring for a scalar field a correct spacial asymptotics that depends on the system mass. Theory, the quantum relation of a corpuscular-wave dualism is fulfilled for soliton solutions in such a model
Nonplanar solitons collision in ultracold neutral plasmas
Energy Technology Data Exchange (ETDEWEB)
El-Tantawy, S. A.; Moslem, W. M.; El-Metwally, M. [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt); Sabry, R. [Theoretical Physics Group, Department of Physics, Faculty of Science, Damietta University, New Damietta 34517 (Egypt); Department of Physics, College of Science and Humanitarian Studies, Salman Bin Abdulaziz University, Alkharj (Saudi Arabia); El-Labany, S. K. [Theoretical Physics Group, Department of Physics, Faculty of Science, Damietta University, New Damietta 34517 (Egypt); Schlickeiser, R. [Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany)
2013-09-15
Collisions between two nonplanar ion-acoustic solitons in strongly coupled ultracold neutral plasmas composed of ion fluid and non-Maxwellian (nonthermal or superthermal) electron distributions are investigated. The extended Poincare-Lighthill-Kuo method is used to obtain coupled nonplanar Kortweg-de Vries equations for describing the system. The nonplanar phase shifts after the interaction of the two solitons are calculated. It is found that the properties of the nonplanar colliding solitons and its corresponding phase shifts are different from those in the planar case. The polarity of the colliding solitons strongly depends on the type of the non-Maxwellian electron distributions. A critical nonthermality parameter β{sub c} is identified. For values of β ≤ β{sub c} solitons with double polarity exist, while this behavior cannot occur for superthermal plasmas. The phase shift for nonthermal plasmas increases below β{sub c} for a positive soliton, but it decreases for β > β{sub c} for a negative soliton. For superthermal plasmas, the phase shift enhances rapidly for low values of spectral index κ and higher values of ions effective temperature ratio σ{sub *}. For 2 ≲ κ<10, the phase shift decreases but does not change for κ > 10. The nonlinear structure, as reported here, is useful for controlling the solitons created in forthcoming ultracold neutral plasma experiments.
Nonplanar solitons collision in ultracold neutral plasmas
El-Tantawy, S. A.; Moslem, W. M.; Sabry, R.; El-Labany, S. K.; El-Metwally, M.; Schlickeiser, R.
2013-09-01
Collisions between two nonplanar ion-acoustic solitons in strongly coupled ultracold neutral plasmas composed of ion fluid and non-Maxwellian (nonthermal or superthermal) electron distributions are investigated. The extended Poincare-Lighthill-Kuo method is used to obtain coupled nonplanar Kortweg-de Vries equations for describing the system. The nonplanar phase shifts after the interaction of the two solitons are calculated. It is found that the properties of the nonplanar colliding solitons and its corresponding phase shifts are different from those in the planar case. The polarity of the colliding solitons strongly depends on the type of the non-Maxwellian electron distributions. A critical nonthermality parameter βc is identified. For values of β ≤ βc solitons with double polarity exist, while this behavior cannot occur for superthermal plasmas. The phase shift for nonthermal plasmas increases below βc for a positive soliton, but it decreases for β > βc for a negative soliton. For superthermal plasmas, the phase shift enhances rapidly for low values of spectral index κ and higher values of ions effective temperature ratio σ*. For 2 ≲ κ 10. The nonlinear structure, as reported here, is useful for controlling the solitons created in forthcoming ultracold neutral plasma experiments.
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
Brownian motion of solitons in a Bose-Einstein condensate.
Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B
2017-03-07
We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.
Kinetic slow mode-type solitons
Directory of Open Access Journals (Sweden)
K. Baumgärtel
2005-01-01
Full Text Available One-dimensional hybrid code simulations are presented, carried out in order both to study solitary waves of the slow mode branch in an isotropic, collisionless, medium-β plasma (βi=0.25 and to test the fluid based soliton interpretation of Cluster observed strong magnetic depressions (Stasiewicz et al., 2003; Stasiewicz, 2004 against kinetic theory. In the simulations, a variety of strongly oblique, large amplitude, solitons are seen, including solitons with Alfvenic polarization, similar to those predicted by the Hall-MHD theory, and robust, almost non-propagating, solitary structures of slow magnetosonic type with strong magnetic field depressions and perpendicular ion heating, which have no counterpart in fluid theory. The results support the soliton-based interpretation of the Cluster observations, but reveal substantial deficiencies of Hall-MHD theory in describing slow mode-type solitons in a plasma of moderate beta.
Vacuum-induced jitter in spatial solitons.
Nagasako, E; Boyd, R; Agarwal, G S
1998-08-31
We perform a calculation to determine how quantum mechanical fluctuations influence the propagation of a spatial soliton through a nonlinear material. To do so, we derive equations of motion for the linearized operators describing the deviation of the soliton position and transverse momentum from those of a corresponding classical solution to the nonlinear wave equation, and from these equations we determine the quantum uncertainty in the soliton position and transverse momentum. We find that under realistic laboratory conditions the quantum uncertainty in position is several orders of magnitude smaller the classical width of the soliton. This result suggests that the reliability of photonic devices based on spatial solitons is not compromised by quantum fluctuations.
Induced waveform transitions of dissipative solitons
Kochetov, Bogdan A.; Tuz, Vladimir R.
2018-01-01
The effect of an externally applied force upon the dynamics of dissipative solitons is analyzed in the framework of the one-dimensional cubic-quintic complex Ginzburg-Landau equation supplemented by a potential term with an explicit coordinate dependence. The potential accounts for the external force manipulations and consists of three symmetrically arranged potential wells whose depth varies along the longitudinal coordinate. It is found out that under an influence of such potential a transition between different soliton waveforms coexisting under the same physical conditions can be achieved. A low-dimensional phase-space analysis is applied in order to demonstrate that by only changing the potential profile, transitions between different soliton waveforms can be performed in a controllable way. In particular, it is shown that by means of a selected potential, stationary dissipative soliton can be transformed into another stationary soliton as well as into periodic, quasi-periodic, and chaotic spatiotemporal dissipative structures.
Ion-acoustic solitons in dusty plasma
Losseva, T. V.; Popel, S. I.; Golub', A. P.
2012-09-01
The dynamics of dust ion-acoustic solitons is analyzed in a wide range of dusty plasma parameters. The cases of both a positive dust grain charge arising due to the photoelectric effect caused by intense electromagnetic radiation and a negative grain charge established in the absence of electromagnetic radiation are considered. The ranges of plasma parameters and Mach numbers in which "conservative" (nondissipative) solitons can exist are determined. It is shown that, in dusty plasma with negatively charged dust grains, both compression and rarefaction solitons can propagate, whereas in plasma with positively charged dust grains, only compression solitons can exist. The evolution of soliton-like compression and rarefaction perturbations is studied by numerically solving the hydrodynamic equations for ions and dust grains, as well as the equation for dust grain charging. The main dissipation mechanisms, such as grain charging, ion absorption by dust grains, momentum exchange between ions and dust grains, and ion-neutral collisions are taken into account. It is shown that the amplitudes of soliton-like compression and rarefaction perturbations decrease in the course of their evolution and their velocities (the Mach numbers) decrease monotonically in time. At any instant of time, the shape of an evolving soliton-like perturbation coincides with the shape of a conservative soliton corresponding to the current value of the Mach number. It is shown that, after the interaction between any types of soliton-like perturbations, their velocities and shapes are restored (with a certain phase shift) to those of the corresponding perturbations propagating without interaction; i.e., they are in fact weakly dissipative solitons.
Interaction of topological solitons with defects: using a nontrivial metric
Energy Technology Data Exchange (ETDEWEB)
Javidan, Kurosh [Department of Physics, Ferdowsi University of Mashhad, 91775-1436 Mashhad (Iran, Islamic Republic of)
2006-08-18
By including a potential into the flat metric, we study the interaction of the sine-Gordon soliton with different potentials. We will show numerically that while the soliton-barrier system shows fully classical behaviour, the soliton-well system demonstrates non-classical behaviour. In particular, solitons with low velocities are trapped in the well and radiate energy. Also for narrow windows of initial velocity, a soliton reflects back from a potential well.
Stability investigation of quadratic systems with delay
Directory of Open Access Journals (Sweden)
Vladimir Davydov
2000-01-01
Full Text Available Systems of differential equations with quadratic right-hand sides with delay are considered in the paper. Compact matrix notation form is proposed for the systems of such type. Stability investigations are performed by Lyapunov's second method with functions of quadratic form. Stability conditions of quadratic systems with delay, uniformly by argument deviation, and with delay depending on the system's parameters are derived. A guaranteed radius of the ball of asymptotic stability region for zero solution is obtained.
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...... source networks and normal dc-dc converters with coupled magnetics at the same duty ratio and turns ratio. The term “Quadratic Boost A-Source” indicates its quadratic varying gain in the operating principle of the converter. The proposed converter draws a continuous current from the source and suits...
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Joint Estimation Using Quadratic Estimating Function
Directory of Open Access Journals (Sweden)
Y. Liang
2011-01-01
of the observed process becomes available, the quadratic estimating functions are more informative. In this paper, a general framework for joint estimation of conditional mean and variance parameters in time series models using quadratic estimating functions is developed. Superiority of the approach is demonstrated by comparing the information associated with the optimal quadratic estimating function with the information associated with other estimating functions. The method is used to study the optimal quadratic estimating functions of the parameters of autoregressive conditional duration (ACD models, random coefficient autoregressive (RCA models, doubly stochastic models and regression models with ARCH errors. Closed-form expressions for the information gain are also discussed in some detail.
Soliton turbulence in shallow water ocean surface waves.
Costa, Andrea; Osborne, Alfred R; Resio, Donald T; Alessio, Silvia; Chrivì, Elisabetta; Saggese, Enrica; Bellomo, Katinka; Long, Chuck E
2014-09-05
We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of soliton turbulence in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a dense soliton gas, described theoretically by the soliton limit of the Korteweg-deVries equation, a completely integrable soliton system: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodic-quasiperiodic boundary conditions the ergodic solutions of Korteweg-deVries are exactly solvable by finite gap theory (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as ∼ω-1. We use the linear Fourier transform to estimate this power law from the power spectrum and to filter densely packed soliton wave trains from the data. We apply FGT to determine the soliton spectrum and find that the low frequency ∼ω-1 region is soliton dominated. The solitons have random FGT phases, a soliton random phase approximation, which supports our interpretation of the data as soliton turbulence. From the probability density of the solitons we are able to demonstrate that the solitons are dense in time and highly non-Gaussian.
Quadratic Lagrangians and Legendre transformation
International Nuclear Information System (INIS)
Magnano, G.
1988-01-01
In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor
The Random Quadratic Assignment Problem
Paul, Gerald; Shao, Jia; Stanley, H. Eugene
2011-11-01
The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.
Gap solitons in Rabi lattices.
Chen, Zhaopin; Malomed, Boris A
2017-03-01
We introduce a two-component one-dimensional system, which is based on two nonlinear Schrödinger or Gross-Pitaevskii equations (GPEs) with spatially periodic modulation of linear coupling ("Rabi lattice") and self-repulsive nonlinearity. The system may be realized in a binary Bose-Einstein condensate, whose components are resonantly coupled by a standing optical wave, as well as in terms of the bimodal light propagation in periodically twisted waveguides. The system supports various types of gap solitons (GSs), which are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. These include on- and off-site-centered solitons (the GSs of the off-site type are additionally categorized as spatially even and odd ones), which may be symmetric or antisymmetric, with respect to the coupled components. The GSs are chiefly stable in the first finite bandgap and unstable in the second one. In addition to that, there are narrow regions near the right edge of the first bandgap, and in the second one, which feature intricate alternation of stability and instability. Unstable solitons evolve into robust breathers or spatially confined turbulent modes. On-site-centered GSs are also considered in a version of the system that is made asymmetric by the Zeeman effect, or by birefringence of the optical waveguide. A region of alternate stability is found in the latter case too. In the limit of strong asymmetry, GSs are obtained in a semianalytical approximation, which reduces two coupled GPEs to a single one with an effective lattice potential.
Chen, Zhaopin; Malomed, Boris A.
2017-03-01
We introduce a two-component one-dimensional system, which is based on two nonlinear Schrödinger or Gross-Pitaevskii equations (GPEs) with spatially periodic modulation of linear coupling ("Rabi lattice") and self-repulsive nonlinearity. The system may be realized in a binary Bose-Einstein condensate, whose components are resonantly coupled by a standing optical wave, as well as in terms of the bimodal light propagation in periodically twisted waveguides. The system supports various types of gap solitons (GSs), which are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. These include on- and off-site-centered solitons (the GSs of the off-site type are additionally categorized as spatially even and odd ones), which may be symmetric or antisymmetric, with respect to the coupled components. The GSs are chiefly stable in the first finite bandgap and unstable in the second one. In addition to that, there are narrow regions near the right edge of the first bandgap, and in the second one, which feature intricate alternation of stability and instability. Unstable solitons evolve into robust breathers or spatially confined turbulent modes. On-site-centered GSs are also considered in a version of the system that is made asymmetric by the Zeeman effect, or by birefringence of the optical waveguide. A region of alternate stability is found in the latter case too. In the limit of strong asymmetry, GSs are obtained in a semianalytical approximation, which reduces two coupled GPEs to a single one with an effective lattice potential.
Generation of two-soliton and three-soliton molecules in a circular fiber array laser
Niknafs, Akram; Rooholamininejad, Hossein; Bahrampour, Alireza
2018-04-01
In this work, the generation of two-soliton and three-soliton molecules in a circular fiber array laser with an active optical central fiber is studied. Certain fibers of the array are excited by Gaussian and super-Gaussian pulses. The central fiber of the circular fiber laser is a rare-earth doped fiber. A circular fiber array is employed as a saturable absorber in a soliton mode locked fiber laser. Generation of two-soliton and three-soliton molecules are observed in our simulation. Numerical calculation of binding energy shows that the super-Gaussian pulse tends to be more stable, and therefore it would be a proper choice for the generation of soliton molecules in the circular fiber array laser.
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.
Fuzzy Objects and Noncommutative Solitons
Kobayashi, Shinpei; Asakawa, Tsuguhiko
2015-01-01
The fuzzy disc is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. We showed that one can introduce a concept of angles to the fuzzy disc, by using the phase operator and phase states known in quantum optics. We also constructed fan-shaped soliton solutions, which would be identified with D-branes, of a scalar field theory on the fuzzy disc and applied this concept to a theory of noncommutative gravity. This proceeding is based on our previous work.
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
Solitons of axion-dilaton gravity
Bakas, Ioannis
1996-01-01
We use soliton techniques of the two-dimensional reduced beta-function equations to obtain non-trivial string backgrounds from flat space. These solutions are characterized by two integers (n, m) referring to the soliton numbers of the metric and axion-dilaton sectors respectively. We show that the Nappi-Witten universe associated with the SL(2) x SU(2) / SO(1, 1) x U(1) CFT coset arises as an (1, 1) soliton in this fashion for certain values of the moduli parameters, while for other values of the soliton moduli we arrive at the SL(2)/SO(1, 1) x SO(1, 1)^2 background. Ordinary 4-dim black-holes arise as 2-dim (2, 0) solitons, while the Euclidean worm-hole background is described as a (0, 2) soliton on flat space. The soliton transformations correspond to specific elements of the string Geroch group. These could be used as starting point for exploring the role of U-dualities in string compactifications to two dimensions.
Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations
Le Coz, Stefan; Tsai, Tai-Peng
2014-11-01
We look for solutions to general nonlinear Schrödinger equations built upon solitons and kinks. Solitons are localized solitary waves, and kinks are their non-localized counter-parts. We prove the existence of infinite soliton trains, i.e. solutions behaving at large time as the sum of infinitely many solitons. We also show that one can attach a kink at one end of the train. Our proofs proceed by fixed point arguments around the desired profile. We present two approaches leading to different results, one based on a combination of Lp - Lp‧ dispersive estimates and Strichartz estimates, the other based only on Strichartz estimates.
Soliton and polaron generation in polyacetylene
International Nuclear Information System (INIS)
Su, Zhao-bin; Yu, Lu.
1984-07-01
The nonradiative decay of an e-h pair into soliton pair and that of an electron (hole) into polaron as well as the photoproduction of soliton pairs are considered using the lattice relaxation theory of multiphonon processes generalized to include the self-consistency of the multi-electron states with the lattice symmetry breaking. The selection rule which forbids the direct process of photogeneration for neutral pair is derived from the symmetry arguments. The branching ratio of the photogenerated neutral to charged soliton pairs is estimated. The recent related experiments are discussed. (author)
Entangled solitons and stochastic Q-bits
International Nuclear Information System (INIS)
Rybakov, Yu.P.; Kamalov, T.F.
2007-01-01
Stochastic realization of the wave function in quantum mechanics with the inclusion of soliton representation of extended particles is discussed. Two-solitons configurations are used for constructing entangled states in generalized quantum mechanics dealing with extended particles, endowed with nontrivial spin S. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein-Podolsky-Rosen (EPR) correlation is calculated and shown to coincide with the quantum mechanical one for the 1/2-spin particles. The concept of stochastic q-bits is used for quantum computing modelling
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....
Topological solitons in DNA with modified potential
Directory of Open Access Journals (Sweden)
E Behjat
2010-06-01
Full Text Available DNA is not only an essential research subject for biologists, but also it raises very interesting questions for physicists.The open states in DNA double helix can lead to topological solitons. Since DNA is a very long molecule of order a meter or so long and nano-scale width, solitons can propagate along the molecule. In this paper, considering a correction term in the interaction potential between two chains, we study the dispersion relation analytically, and obtain the soliton solutions using a new relaxation method. Then we compare our solutions and its energy with those obtained by others without the proposed correction term.
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......NL to demonstrate a significant soliton selffrequency shift of a fundamental soliton, and we show that nonlinear matching can take precedence over linear mode matching. The nonlinear coupling coefficient depends on both the dispersion (β2) and nonlinearity (γ), as well as on the power coupling efficiency η. Being...
Intensity noise coupling in soliton fiber oscillators.
Wan, Chenchen; Schibli, Thomas R; Li, Peng; Bevilacqua, Carlo; Ruehl, Axel; Hartl, Ingmar
2017-12-15
We present an experimental and numerical study on the spectrally resolved pump-to-output intensity noise coupling in soliton fiber oscillators. In our study, we observe a strong pump noise coupling to the Kelly sidebands, while the coupling to the soliton pulse is damped. This behavior is observed in erbium-doped as well as holmium-doped fiber oscillators and confirmed by numerical modeling. It can be seen as a general feature of laser oscillators in which soliton pulse formation is dominant. We show that spectral blocking of the Kelly sidebands outside the laser cavity can improve the intensity noise performance of the laser dramatically.
Time-space noncommutative Abelian solitons
International Nuclear Information System (INIS)
Chu, C.-S.; Lechtenfeld, Olaf
2005-01-01
We demonstrate the construction of solitons for a time-space Moyal-deformed integrable U(n) sigma model (the Ward model) in 2+1 dimensions. These solitons cannot travel parallel to the noncommutative spatial direction. For the U(1) case, the rank-one single-soliton configuration is constructed explicitly and is singular in the commutative limit. The projection to 1+1 dimensions transforms it to a noncommutative instanton-like configuration. The latter is governed by a new integrable equation, which describes a Moyal-deformed sigma model with a particular Euclidean metric and a magnetic field
Solitons in Gross-Pitaevskii equation
International Nuclear Information System (INIS)
Lopes, E.
1985-01-01
It is observed that, when the potential is integrable and repulsive, the Gross-Pitaevskii Equation, with non-vanishing boundary conditions, describes a family of planar solitons. A method is presented which provides an exact soliton field to the Dirac Delta potential and an approximation solution to any other kind of potential. As an example the method is then applied to the case of a repulsive Yukawa potential. A brief discuss the relation between these solitons and Anderson's superfluidity mechanism, is also presented. (author) [pt
Soliton cellular automata associated with crystal bases
International Nuclear Information System (INIS)
Hatayama, Goro; Kuniba, Atsuo; Takagi, Taichiro
2000-01-01
We introduce a class of cellular automata associated with crystals of irreducible finite dimensional representations of quantum affine algebras U' q (g-circumflex n ). They have solitons labeled by crystals of the smaller algebra U' q (g-circumflex n-1 ). We prove stable propagation of one soliton for g-circumflex n =A (2) 2n-1 ,A (2) 2n ,B (1) n ,C (1) n ,D (1) n and D (2) n+1 . For g-circumflex n =C (1) n , we also prove that the scattering matrices of two solitons coincide with the combinatorial R matrices of U' q (C (1) n-1 )-crystals
orthogonal and scaling transformations of quadratic functions
African Journals Online (AJOL)
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ABSTRACT: In this paper we present a non-singular transformation that can reduce a given quadratic function defined on n. R to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that ...
Quadratic independence of coordinate functions of certain ...
Indian Academy of Sciences (India)
... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.
Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...
African Journals Online (AJOL)
Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme
Bound constrained quadratic programming via piecewise
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.
1999-01-01
We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...
A Note on Cooperative Linear Quadratic Control
Engwerda, J.C.
2007-01-01
In this note we consider the cooperative linear quadratic control problem. That is, the problem where a number of players, all facing a (different) linear quadratic control problem, decide to cooperate in order to optimize their performance. It is well-known, in case the performance criteria are
An Unexpected Influence on a Quadratic
Davis, Jon D.
2013-01-01
Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…
Quadratic Hedging of Basis Risk
Directory of Open Access Journals (Sweden)
Hardy Hulley
2015-02-01
Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.
Successive soliton explosions in an ultrafast fiber laser.
Liu, Meng; Luo, Ai-Ping; Yan, Yu-Rong; Hu, Song; Liu, Yi-Chen; Cui, Hu; Luo, Zhi-Chao; Xu, Wen-Cheng
2016-03-15
Soliton explosions, as one of the most fascinating nonlinear phenomena in dissipative systems, have been investigated in different branches of physics, including the ultrafast laser community. Herein, we reported on the soliton dynamics of an ultrafast fiber laser from steady state to soliton explosions, and to huge explosions by simply adjusting the pump power level. In particular, the huge soliton explosions show that the exploding behavior could operate in a sustained, but periodic, mode from one explosion to another, which we term as "successive soliton explosions." The experimental results will prove to be fruitful to the various communities interested in soliton explosions.
Nonlinear Dynamics: Maps, Integrators and Solitons
Energy Technology Data Exchange (ETDEWEB)
Parsa, Z.
1998-10-01
For many physical systems of interest in various disciplines, the solution to nonlinear differential equations describing the physical systems can be generated using maps, symplectic integrators and solitons. We discuss these methods and apply them for various examples.
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.
Cascade annealing: an overview
International Nuclear Information System (INIS)
Doran, D.G.; Schiffgens, J.O.
1976-04-01
Concepts and an overview of radiation displacement damage modeling and annealing kinetics are presented. Short-term annealing methodology is described and results of annealing simulations performed on damage cascades generated using the Marlowe and Cascade programs are included. Observations concerning the inconsistencies and inadequacies of current methods are presented along with simulation of high energy cascades and simulation of longer-term annealing
Solitons in an isolated helix chain
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Zolotaryuk, Alexander; Savin, A.V.
1997-01-01
-, and third-nearest neighbors. The set of nonlinear field equations with respect to the longitudinal and transverse (torsional and radial) displacements of the chain molecules has been derived and treated. Stable nontopological soliton solutions which describe supersonic pulses of longitudinal compression...... propagating together with localized transverse thickening (bulge) and torsional stretching (untwisting) have been found. The stability properties of these (three-component) soliton solutions have been studied by using numerical techniques developed for seeking solitary-wave solutions in complex molecular...
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....
Soliton/exciton transport in proteins.
Sinkala, Zachariah
2006-08-21
The study of electron/proton transport in alpha-helix sections of proteins have illustrated the existence of soliton-like mechanisms. Recently, Ciblis and Cosic extended investigation to the existence of possible like soliton-type mechanisms in other parts of the protein. They used Quantum Hamiltonian analysis to investigate. In this paper, we investigate the same problem but we use Classical Hamiltonian analysis in our investigation.
Stable helical solitons in optical media
Indian Academy of Sciences (India)
case is when the centres of the colliding solitons exactly coincide atz =0. In this case, δωl is found by straightforward integration of eq. (14) from z = 0 to z = +∞. The result can be presented in a more natural form, multiplying the net frequency shift by the soliton's temporal width (i.e., normalizing the frequency shift to the ...
Soliton dynamics in the multiphoton plasma regime
Husko, Chad A.; Combrié, Sylvain; Colman, Pierre; Zheng, Jiangjun; De Rossi, Alfredo; Wong, Chee Wei
2013-01-01
Solitary waves have consistently captured the imagination of scientists, ranging from fundamental breakthroughs in spectroscopy and metrology enabled by supercontinuum light, to gap solitons for dispersionless slow-light, and discrete spatial solitons in lattices, amongst others. Recent progress in strong-field atomic physics include impressive demonstrations of attosecond pulses and high-harmonic generation via photoionization of free-electrons in gases at extreme intensities of 1014 W/cm2. Here we report the first phase-resolved observations of femtosecond optical solitons in a semiconductor microchip, with multiphoton ionization at picojoule energies and 1010 W/cm2 intensities. The dramatic nonlinearity leads to picojoule observations of free-electron-induced blue-shift at 1016 cm−3 carrier densities and self-chirped femtosecond soliton acceleration. Furthermore, we evidence the time-gated dynamics of soliton splitting on-chip, and the suppression of soliton recurrence due to fast free-electron dynamics. These observations in the highly dispersive slow-light media reveal a rich set of physics governing ultralow-power nonlinear photon-plasma dynamics.
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.)
Models of few optical cycle solitons beyond the slowly varying envelope approximation
Energy Technology Data Exchange (ETDEWEB)
Leblond, H., E-mail: herve.leblond@univ-angers.fr [LUNAM University, Université d’Angers, Laboratoire de Photonique d’Angers, EA 4464, 2 Bd. Lavoisier, 49045 Angers Cedex 01 (France); Mihalache, D. [LUNAM University, Université d’Angers, Laboratoire de Photonique d’Angers, EA 4464, 2 Bd. Lavoisier, 49045 Angers Cedex 01 (France); Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, 077125 Magurele (Romania); Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest (Romania)
2013-02-15
In the past years there was a huge interest in experimental and theoretical studies in the area of few-optical-cycle pulses and in the broader fast growing field of the so-called extreme nonlinear optics. This review concentrates on theoretical studies performed in the past decade concerning the description of few optical cycle solitons beyond the slowly varying envelope approximation (SVEA). Here we systematically use the powerful reductive expansion method (alias multiscale analysis) in order to derive simple integrable and nonintegrable evolution models describing both nonlinear wave propagation and interaction of ultrashort (femtosecond) pulses. To this aim we perform the multiple scale analysis on the Maxwell–Bloch equations and the corresponding Schrödinger–von Neumann equation for the density matrix of two-level atoms. We analyze in detail both long-wave and short-wave propagation models. The propagation of ultrashort few-optical-cycle solitons in quadratic and cubic nonlinear media are adequately described by generic integrable and nonintegrable nonlinear evolution equations such as the Korteweg–de Vries equation, the modified Korteweg–de Vries equation, the complex modified Korteweg–de Vries equation, the sine–Gordon equation, the cubic generalized Kadomtsev–Petviashvili equation, and the two-dimensional sine–Gordon equation. Moreover, we consider the propagation of few-cycle optical solitons in both (1+1)- and (2+1)-dimensional physical settings. A generalized modified Korteweg–de Vries equation is introduced in order to describe robust few-optical-cycle dissipative solitons. We investigate in detail the existence and robustness of both linearly polarized and circularly polarized few-cycle solitons, that is, we also take into account the effect of the vectorial nature of the electric field. Some of these results concerning the systematic use of the reductive expansion method beyond the SVEA can be relatively easily extended to few
Seven Wonders of the Ancient and Modern Quadratic World.
Taylor, Sharon E.; Mittag, Kathleen Cage
2001-01-01
Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)
Two-soliton and three-soliton interactions of electron acoustic waves ...
Indian Academy of Sciences (India)
Electron acoustic wave; quantum plasma; two-soliton; three-soliton; overtaking collision; phase shift; Hirota bilinear method. ... Birbhum 731 301, India; Department of Physics, Darjeeling Government College, Darjeeling 734 104, India; Department of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan 731 ...
Two-soliton and three-soliton interactions of electron acoustic waves ...
Indian Academy of Sciences (India)
Electron acoustic wave; quantum plasma; two-soliton; three-soliton; overtaking collision; phase shift; Hirota bilinear method. PACS Nos 52.27.−h; 52.35.−g; 52.35.Sb. 1. Introduction. The mathematical modelling of physical phenomena often leads to nonlinear evolution equations. It is worth mentioning that many of these ...
Dynamics of charges and solitons
Barros, Manuel; Ferrández, Ángel; Garay, Óscar J.
2018-02-01
We first show that trajectories traced by charges moving in rotational magnetic fields are, basically, the non-parallel geodesics of surfaces of revolution with coincident axis. Thus, people living in a surface of revolution are not able to sense the magnetic Hall effect induced by the surrounding magnetic field and perceive charges as influenced, exclusively, by the gravity action on the surface of revolution. Secondly, the extended Hasimoto transformations are introduced and then used to identify trajectories of charges moving through a Killing rotational magnetic field in terms of non-circular elastic curves. As a consequence, we see that in this case charges evolve along trajectories which are obtained as extended Hasimoto transforms of solitons of the filament equation.
International Nuclear Information System (INIS)
Wilets, L.; Goldflam, R.
1983-09-01
The MIT bag was one of the earliest and most successful models of QCD, imposing confinement and including perturbative gluon interactions. An evolution of the MIT bag came with the introduction of the chiral and cloudy bags, which treat pions as elementary particles. As a model of QCD, the soliton model proposed by Friedberg and Lee is particularly attractive. It is based on a covariant field theory and is sufficiently general so that, for certain limiting cases of the adjustable parameters, it can describe either the MIT or SLAC (string) bags. The confinement mechanism appears as a dynamic field. This allows non-static processes, such as bag oscillations and bag collisions, to be calculated utilizing the well-developed techniques of nuclear many-body theory. The utilization of the model for calculating dynamical processes is discussed. 14 references
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
Solitons in a Dielectric Medium under an External Magnetic Field
Isamu, NAKATA; Hiroaki, ONO; Mitito, YOSIDA; College of Integrated Arts and Sciences, University of Osaka Prefecture; Department of Mathematics and Physics, Faculty of Engineering, Setunan University; Nippondenso Co., Ltd.
1993-01-01
Solitons in a dielectric medium propagating along an external magnetic field is investigated. By means of a nonlinear perturbation method, the derivative nonlinear Schrodinger equation is derived and the possibility of propagation of the spiky and algebraic solitons is shown.
On soliton solutions of the Wu-Zhang system
Directory of Open Access Journals (Sweden)
Inc Mustafa
2016-01-01
Full Text Available In this paper, the extended tanh and hirota methods are used to construct soliton solutions for the WuZhang (WZ system. Singular solitary wave, periodic and multi soliton solutions of the WZ system are obtained.
Inelastic Vector Soliton Collisions: A Lattice-Based Quantum Representation
National Research Council Canada - National Science Library
Vahala, George; Vahala, Linda; Yepez, Jeffrey
2004-01-01
.... Under appropriate conditions the exact 2-soliton vector solutions yield in elastic soliton collisions, in agreement with the theoretical predictions of Radhakrishnan et al. (1997 Phys. Rev. E56, 2213...
Perturbative effects on ultra-short soliton self-switching
Indian Academy of Sciences (India)
short soliton self-switching. AMARENDRA K SARMA. 1,∗ and AJIT KUMAR. 2. 1. Department of ... Abstract. A numerical study of ultra-short self-soliton switching along with the corre- ..... improving the presentation of our work. References.
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
Quadratic Equations...Origins, Development and Use.
McQualter, J. W.
1988-01-01
There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (YP)
Schur Stability Regions for Complex Quadratic Polynomials
Cheng, Sui Sun; Huang, Shao Yuan
2010-01-01
Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)
Vector soliton fission by reflection at nonlinear interfaces
Ye, Fangwei; Kartashov, Yaroslav V.; Torner, Lluis
2006-01-01
We address the reflection of vector solitons, comprising several components that exhibit multiple field oscillations, at the interface between two nonlinear media. We reveal that reflection causes fission of the input signal into sets of solitons propagating at different angles. We find that the maximum number of solitons that arises upon fission is given by the number of field oscillations in the highest-order input vector soliton. Peer Reviewed
Nonlocal gap soliton in liquid infiltrated photonic crystal fibres
DEFF Research Database (Denmark)
Bennet, F.H.; Rosberg, C.R.; Rasmussen, Per Dalgaard
We report on the observation of nonlocal gap solitons in infiltrated photonic crystal fibres. We employ the thermal defocusing nonlinearity of the liquid to study soliton existence and effect of boundaries of the periodic structure.......We report on the observation of nonlocal gap solitons in infiltrated photonic crystal fibres. We employ the thermal defocusing nonlinearity of the liquid to study soliton existence and effect of boundaries of the periodic structure....
Peregrine soliton generation and breakup in standard telecommunications fiber.
Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Morin, Philippe; Fatome, Julien; Dudley, John M; Millot, Guy
2011-01-15
We present experimental and numerical results showing the generation and breakup of the Peregrine soliton in standard telecommunications fiber. The impact of nonideal initial conditions is studied through direct cutback measurements of the longitudinal evolution of the emerging soliton dynamics and is shown to be associated with the splitting of the Peregrine soliton into two subpulses, with each subpulse itself exhibiting Peregrine soliton characteristics. Experimental results are in good agreement with simulations.
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....
Radiotherapy treatment planning linear-quadratic radiobiology
Chapman, J Donald
2015-01-01
Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil
BOOK REVIEW: Solitons, Instantons, and Twistors Solitons, Instantons, and Twistors
Witt, Donald M.
2011-04-01
Solitons and instantons play important roles both in pure and applied mathematics as well as in theoretical physics where they are related to the topological structure of the vacuum. Twistors are a useful tool for solving nonlinear differential equations and are useful for the study of the antiself-dual Yang-Mills equations and the Einstein equations. Many books and more advanced monographs have been written on these topics. However, this new book by Maciej Dunajski is a complete first introduction to all of the topics in the title. Moreover, it covers them in a very unique way, through integrable systems. The approach taken in this book is that of mathematical physics à la field theory. The book starts by giving an introduction to integrable systems of ordinary and partial differential equations and proceeds from there. Gauge theories are not covered until chapter 6 which means the reader learning the material for the first time can build up confidence with simpler models of solitons and instantons before encountering them in gauge theories. The book also has an extremely clear introduction to twistor theory useful to both mathematicians and physicists. In particular, the twistor theory presentation may be of interest to string theorists wanting understand twistors. There are many useful connections to research into general relativity. Chapter 9 on gravitational instantons is great treatment useful to anyone doing research in classical or quantum gravity. There is also a nice discussion of Kaluza-Klein monopoles. The three appendices A-C cover the necessary background material of basic differential geometry, complex manifolds, and partial differential equations needed to fully understand the subject. The reader who has some level of expertise in any of the topics covered can jump right into that material without necessarily reading all of the earlier chapters because of the extremely clear writing style of the author. This makes the book an excellent reference on
Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation
Stalin, S.; Senthilvelan, M.
2012-01-01
In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno. By appropriately modifying the $\\tau$-function given in the above paper we derive these solutions. We present the explicit form of one and two loop soliton solutions and mixed soliton - loop soliton solutions and investigate the interaction between (i) two loop soliton solutions in different para...
Universal soliton pattern formations in passively mode-locked fiber lasers.
Amrani, Foued; Salhi, Mohamed; Grelu, Philippe; Leblond, Hervé; Sanchez, François
2011-05-01
We investigate multiple-soliton pattern formations in a figure-of-eight passively mode-locked fiber laser. Operation in the anomalous dispersion regime with a double-clad fiber amplifier allows generation of up to several hundreds of solitons per round trip. We report the observation of remarkable soliton distributions: soliton gas, soliton liquid, soliton polycrystal, and soliton crystal, thus indicating the universality of such complexes.
Bistable soliton states and switching in doubly inhomogeneously ...
Indian Academy of Sciences (India)
Bistable soliton states and switching in doubly inhomogeneously doped ﬁber couplers. Ajit Kumar. Theoretical aspects of optical solitons Volume 57 Issue 5-6 November-December 2001 pp 969-979 ... Switching between the bistable soliton states in a doubly and inhomogeneously doped ﬁber system is studied numerically.
Protocol of networks using energy sharing collisions of bright solitons
Indian Academy of Sciences (India)
physics pp. 1009–1021. Protocol of networks using energy sharing collisions of bright solitons. K NAKAMURA1,2, T KANNA3,∗ and K SAKKARAVARTHI3. 1Faculty of Physics ... solitonic collisions is expected and therefore multiple soliton dynamics leads to a triv- ..... One can obtain various choices of αk which satisfy eq.
Soliton-based ultra-high speed optical communications
Indian Academy of Sciences (India)
All these facts are the outcome of research on optical solitons in ﬁbers in spite of the fact that the commonly used RZ format is not always called a soliton format. The overview presented here attempts to incorporate the role of soliton-based communications research in present day ultra-high speed communications.
Experimental Investigation of Trapped Sine-Gordon Solitons
DEFF Research Database (Denmark)
Davidson, A.; Dueholm, B.; Kryger, B.
1985-01-01
We have observed for the first time a single sine-Gordon soliton trapped in an annular Josephson junction. This system offers a unique possibility to study undisturbed soliton motion. In the context of perturbation theory, the soliton may be viewed as a relativistic particle moving under a uniform...
Dynamics of coupled field solitons: A collective coordinate approach
Indian Academy of Sciences (India)
Danial Saadatmand, Aliakbar Moradi Marjaneh and Mahdi Heidari. The above equations show that the peak of each soliton moves under the influence of complicated forces which are functions of external potentials and the positions of solitons. Suppose that a soliton moves toward a potential barrier. Its velocity will reduce ...
Analysis and design of fibers for pure-quartic solitons
DEFF Research Database (Denmark)
Lo, Chih-Wei; Stefani, Alessio; de Sterke, C. Martijn
2018-01-01
-quartic solitons in optical platforms. We apply this analysis, in combination with numerical calculations, to the design of pure-quartic soliton supporting microstructured optical fibers. The designs presented here, which have realistic fabrication tolerances, support unperturbed pure-quartic soliton propagation...
Peng, Junsong; Tarasov, Nikita; Sugavanam, Srikanth; Churkin, Dmitry
2016-09-19
We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.
DEFF Research Database (Denmark)
Zhou, B. B.; Chong, A.; Wise, F. W.
2012-01-01
response with an octave-spanning bandwidth. We verify this experimentally by showing few-cycle soliton compression with noncritical cascaded second-harmonic generation: Energetic 47 fs infrared pulses are compressed in a just 1-mm long bulk lithium niobate crystal to 17 fs (under 4 optical cycles) with 80......% efficiency, and upon further propagation an octave-spanning supercontinuum is observed. Such ultrafast cascading is expected to occur for a broad range of pump wavelengths spanning the near- and mid-IR using standard nonlinear crystals....
Marquez, Enrique, Salvador; Hare, Jonathon; Niranjan, Mahesan
2018-01-01
In this paper, we propose a novel approach for efficient training of deep neural networks in a bottom-up fashion using a layered structure. Our algorithm, which we refer to as Deep Cascade Learning, is motivated by the Cascade Correlation approach of Fahlman who introduced it in the context of perceptrons. We demonstrate our algorithm on networks of convolutional layers, though its applicability is more general. Such training of deep networks in a cascade, directly circumvents the well-know...
Nucleon described by the chiral soliton in the chiral quark soliton model
Watabe, T.; Goeke, K.
1998-02-01
We give a survey of recent development and applications of the chiral quark soliton model (also called the Nambu-Jona-Lasinio soliton model) with N f=2 and N f=3 quark flavors for the structure of baryons. The model is an effective chiral quark model obtained from the instanton liquid model of the quantum chromodynamics. Mesons appear as quark-antiquark excitations and baryons arise as non-topological solitons with three valence quarks and a polarized Dirac sea. In this model, a wide variety of observables of baryons is considered.
Nucleon described by the chiral soliton in the chiral quark soliton model
Energy Technology Data Exchange (ETDEWEB)
Watabe, T.; Goeke, K. [Ruhr-Univ., Bochum (Germany). Inst. fur Theor. Phys. II
1998-02-02
We give a survey of recent development and applications of the chiral quark soliton model (also called the Nambu-Jona-Lasinio soliton model) with N{sub f} = 2 and N{sub f} = 3 quark flavors for the structure of baryons. The model is an effective chiral quark model obtained from the instanton liquid model of the quantum chromodynamics. Mesons appear as quark-antiquark excitations and baryons arise as non-topological solitons with three valence quarks and a polarized Dirac sea. In this model, a wide variety of observables of baryons is considered. (orig.). 12 refs.
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.
280 GHz dark soliton fiber laser.
Song, Y F; Guo, J; Zhao, L M; Shen, D Y; Tang, D Y
2014-06-15
We report on an ultrahigh repetition rate dark soliton fiber laser. We show both numerically and experimentally that by taking advantage of the cavity self-induced modulation instability and the dark soliton formation in a net normal dispersion cavity fiber laser, stable ultrahigh repetition rate dark soliton trains can be formed in a dispersion-managed cavity fiber laser. Stable dark soliton trains with a repetition rate as high as ∼280 GHz have been generated in our experiment. Numerical simulations have shown that the effective gain bandwidth limitation plays an important role on the stabilization of the formed dark solitons in the laser.
An(1) Toda solitons and the dressing symmetry
International Nuclear Information System (INIS)
Belich, H.; Paunov, R.
1996-12-01
We present an elementary derivation of the soliton-like solutions in the A n (1) Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are calculated. This enables us to obtain explicit expression for the element which by dressing group action, produces a generic soliton solution. In the particular example of mono solitons we suggest a relation to vertex operator formalism, previously used by olive, Turok and Underwood. Our results can also be considered as generalization of the approach to the sine-Gordon solitons, proposed by Babelon and Bernard. (author)
Stable two-dimensional dispersion-managed soliton
International Nuclear Information System (INIS)
Abdullaev, Fatkhulla Kh.; Baizakov, Bakhtiyor B.; Salerno, Mario
2003-01-01
The existence of a dispersion-managed soliton in two-dimensional nonlinear Schroedinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown
The Factorability of Quadratics: Motivation for More Techniques
Bosse, Michael J.; Nandakumar, N. R.
2005-01-01
Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…
Modification of ion-acoustic solitons on interaction with Langmuir waves
International Nuclear Information System (INIS)
Basovich, A.Ya.; Gromov, E.M.; Karpman, V.I.
1981-01-01
Variation of an ion-accoustic soliton under the effect of the Langmuir quasimonochromatic wave has been considered. Parameters of the soliton tail and variation of soliton velocity have been determined. It is shown that the soliton tail consists of two parts: averaged and oscillating. Density oscillations have a forced nature and are related to the modulation of striction force appearing during interference of waves incident and reflected from a soliton. Oscillations appear behind soliton when the wave runs after soliton and in front of soliton when soliton runs after wave [ru
Dissipative solitons in pair-ion plasmas
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Samiran, E-mail: sran-g@yahoo.com [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Adak, Ashish, E-mail: ashish-adak@yahoo.com; Khan, Manoranjan, E-mail: mkhan.ju@gmail.com [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India)
2014-01-15
The effects of ion-neutral collisions on the dynamics of the nonlinear ion acoustic wave in pair-ion plasma are investigated. The standard perturbative approach leads to a Korteweg-de Vries equation with a linear damping term for the dynamics of the finite amplitude wave. The ion-neutral collision induced dissipation is responsible for the linear damping. The analytical solution and numerical simulation reveal that the nonlinear wave propagates in the form of a weakly dissipative compressive solitons. Furthermore, the width of the soliton is proportional to the amplitude of the wave for fixed soliton velocity. Results are discussed in the context of the fullerene pair-ion plasma experiment.
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 frequ......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...
Introduction to soliton theory applications to mechanics
Munteanu, Ligia
2005-01-01
This monograph provides the application of soliton theory to solve certain problems selected from the fields of mechanics. The work is based of the authors' research, and on some specified, significant results existing in the literature. The present monograph is not a simple translation of its predecessor appeared in Publishing House of the Romanian Academy in 2002. Improvements outline the way in which the soliton theory is applied to solve some engineering problems. The book addresses concrete resolution methods of certain problems such as the motion of thin elastic rod, vibrations of initial deformed thin elastic rod, the coupled pendulum oscillations, dynamics of left ventricle, transient flow of blood in arteries, the subharmonic waves generation in a piezoelectric plate with Cantor-like structure, and some problems related to Tzitzeica surfaces. This comprehensive study enables the readers to make connections between the soliton physical phenomenon and some partical, engineering problems.
Quantization ambiguities of the SU(3) soliton
Praszał Owicz, M.; Watabe, T.; Goeke, K.
1999-03-01
We reconsider canonical quantization of the rotating soliton in the SU(3) chiral quark-soliton model. We show that at the level of {1}/{N c}, in contrast to the SU(2) version of the model, there appear terms which spoil the commutation rules of the flavor generators. Terms of similar origin are also present in the expressions for axial couplings and magnetic moments. We investigate the small soliton limit of the model, and require that the results for the physical observables reduce to the ones of the non-relativistic quark model. This procedure allows us to identify the troublesome terms. Next, we introduce a symmetry conserving approach which consists in subtracting the previously identified terms.
Quantization ambiguities of the SU(3) soliton
Energy Technology Data Exchange (ETDEWEB)
Praszalowicz, M.; Watabe, T.; Goeke, K
1999-03-01
We reconsider canonical quantization of the rotating soliton in the SU(3) chiral quark-soliton model. We show that at the level of 1/N{sub c}, in contrast to the SU(2) version of the model, there appear terms which spoil the commutation rules of the flavor generators. Terms of similar origin are also present in the expressions for axial couplings and magnetic moments. We investigate the small soliton limit of the model, and require that the results for the physical observables reduce to the ones of the non-relativistic quark model. This procedure allows us to identify the troublesome terms. Next, we introduce a symmetry conserving approach which consists in subtracting the previously identified terms.
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2006-01-01
This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...
Linear-quadratic control and quadratic differential forms for multidimensional behaviors
Napp, D.; Trentelman, H.L.
2011-01-01
This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look
Moving solitons in a one-dimensional fermionic superfluid
Efimkin, Dmitry K.; Galitski, Victor
2015-02-01
A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov-de Gennes equations, which are solved exactly in the Andreev approximation. The soliton manifests itself in a kinklike profile of the superconducting order parameter and hosts a pair of Andreev bound states in its core. They adjust to the soliton's motion and play an important role in its stabilization. A phase jump across the soliton and its energy decrease with the soliton's velocity and vanish at the critical velocity, corresponding to the Landau criterion, where the soliton starts emitting quasiparticles and becomes unstable. The "inertial" and "gravitational" masses of the soliton are calculated and the former is shown to be orders of magnitude larger than the latter. This results in a slow motion of the soliton in a harmonic trap, reminiscent of the observed behavior of a solitonlike texture in related experiments in cold fermion gases [T. Yefsah et al., Nature (London) 499, 426 (2013), 10.1038/nature12338]. Furthermore, we calculate the full nonlinear dispersion relation of the soliton and solve the classical equations of motion in a trap. The strong nonlinearity at high velocities gives rise to anharmonic oscillatory motion of the soliton. A careful analysis of this anharmonicity may provide a means to experimentally measure the nonlinear soliton spectrum in superfluids.
Holography for field theory solitons
Domokos, Sophia K.; Royston, Andrew B.
2017-07-01
We extend a well-known D-brane construction of the AdS/dCFT correspondence to non-abelian defects. We focus on the bulk side of the correspondence and show that there exists a regime of parameters in which the low-energy description consists of two approximately decoupled sectors. The two sectors are gravity in the ambient spacetime, and a six-dimensional supersymmetric Yang-Mills theory. The Yang-Mills theory is defined on a rigid AdS4 × S 2 background and admits sixteen supersymmetries. We also consider a one-parameter deformation that gives rise to a family of Yang-Mills theories on asymptotically AdS4 × S 2 spacetimes, which are invariant under eight supersymmetries. With future holographic applications in mind, we analyze the vacuum structure and perturbative spectrum of the Yang-Mills theory on AdS4 × S 2, as well as systems of BPS equations for finite-energy solitons. Finally, we demonstrate that the classical Yang-Mills theory has a consistent truncation on the two-sphere, resulting in maximally supersymmetric Yang-Mills on AdS4.
Soliton models for thick branes
Energy Technology Data Exchange (ETDEWEB)
Peyravi, Marzieh [Ferdowsi University of Mashhad, Department of Physics, School of Sciences, Mashhad (Iran, Islamic Republic of); Riazi, Nematollah [Shahid Beheshti University, Physics Department, Tehran (Iran, Islamic Republic of); Lobo, Francisco S.N. [Faculdade de Ciencias da Universidade de Lisboa, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal)
2016-05-15
In this work, we present new soliton solutions for thick branes in 4+1 dimensions. In particular, we consider brane models based on the sine-Gordon (SG), φ{sup 4} and φ{sup 6} scalar fields, which have broken Z{sub 2} symmetry in some cases and are responsible for supporting and stabilizing the thick branes. The origin of the symmetry breaking in these models resides in the fact that the modified scalar field potential may have non-degenerate vacua. These vacua determine the cosmological constant on both sides of the brane. We also study the geodesic equations along the fifth dimension, in order to explore the particle motion in the neighborhood of the brane. Furthermore, we examine the stability of the thick branes, by determining the sign of the w{sup 2} term in the expansion of the potential for the resulting Schroedinger-like equation, where w is the five-dimensional coordinate. It turns out that the φ{sup 4} brane is stable, while there are unstable modes for certain ranges of the model parameters in the SG and φ{sup 6} branes. (orig.)
Cascaded automatic target recognition (Cascaded ATR)
Walls, Bradley
2010-04-01
The global war on terror has plunged US and coalition forces into a battle space requiring the continuous adaptation of tactics and technologies to cope with an elusive enemy. As a result, technologies that enhance the intelligence, surveillance, and reconnaissance (ISR) mission making the warfighter more effective are experiencing increased interest. In this paper we show how a new generation of smart cameras built around foveated sensing makes possible a powerful ISR technique termed Cascaded ATR. Foveated sensing is an innovative optical concept in which a single aperture captures two distinct fields of view. In Cascaded ATR, foveated sensing is used to provide a coarse resolution, persistent surveillance, wide field of view (WFOV) detector to accomplish detection level perception. At the same time, within the foveated sensor, these detection locations are passed as a cue to a steerable, high fidelity, narrow field of view (NFOV) detector to perform recognition level perception. Two new ISR mission scenarios, utilizing Cascaded ATR, are proposed.
Group-velocity-locked vector soliton molecules in fiber lasers.
Luo, Yiyang; Cheng, Jianwei; Liu, Bowen; Sun, Qizhen; Li, Lei; Fu, Songnian; Tang, Dingyuan; Zhao, Luming; Liu, Deming
2017-05-24
Physics phenomena of multi-soliton complexes have enriched the life of dissipative solitons in fiber lasers. By developing a birefringence-enhanced fiber laser, we report the first experimental observation of group-velocity-locked vector soliton (GVLVS) molecules. The birefringence-enhanced fiber laser facilitates the generation of GVLVSs, where the two orthogonally polarized components are coupled together to form a multi-soliton complex. Moreover, the interaction of repulsive and attractive forces between multiple pulses binds the particle-like GVLVSs together in time domain to further form compound multi-soliton complexes, namely GVLVS molecules. By adopting the polarization-resolved measurement, we show that the two orthogonally polarized components of the GVLVS molecules are both soliton molecules supported by the strongly modulated spectral fringes and the double-humped intensity profiles. Additionally, GVLVS molecules with various soliton separations are also observed by adjusting the pump power and the polarization controller.
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...... exactly implies phase as well as group-velocity matching between the input soliton and tunneled soliton, namely a soliton phase matching condition. Examples in realistic photonic crystal fibers are also presented....
Single-qubit remote manipulation by magnetic solitons
Energy Technology Data Exchange (ETDEWEB)
Cuccoli, Alessandro, E-mail: cuccoli@fi.infn.it [Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); CNISM – c/o Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Nuzzi, Davide, E-mail: nuzzi@fi.infn.it [Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Vaia, Ruggero, E-mail: ruggero.vaia@isc.cnr.it [Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Verrucchi, Paola, E-mail: verrucchi@fi.infn.it [Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy)
2016-02-15
Magnetic solitons can constitute a means for manipulating qubits from a distance. This would overcome the necessity of directly applying selective magnetic fields, which is unfeasible in the case of a matrix of qubits embedded in a solid-state quantum device. If the latter contained one-dimensional Heisenberg spin chains coupled to each qubit, one can originate a soliton in a selected chain by applying a time-dependent field at one end of it, far from the qubits. The generation of realistic solitons has been simulated. When a suitable soliton passes by, the coupled qubit undergoes nontrivial operations, even in the presence of moderate thermal noise. - Highlights: • Proposal for the remote control of qubits coupled to a spin chain supporting solitons. • Traveling solitons can be generated on the chain by acting far from the qubit. • Suitable magnetic solitons can properly change the qubit state. • This qubit manipulation mechanism is shown to be resilient to thermal noise.
Massive WDM and TDM Soliton Transmission Systems : a ROSC Symposium
2002-01-01
This book summarizes the proceedings of the invited talks presented at the “International Symposium on Massive TDM and WDM Optical Soliton Tra- mission Systems” held in Kyoto during November 9–12, 1999. The symposium is the third of the series organized by Research Group for Optical Soliton C- munications (ROSC) chaired by Akira Hasegawa. The research group, ROSC, was established in Japan in April 1995 with a support of the Japanese Ministry of Post and Telecommunications to promote collaboration and information - change among communication service companies, communication industries and academic circles in the theory and application of optical solitons. The symposium attracted enthusiastic response from worldwide researchers in the field of soliton based communications and intensive discussions were made. In the symposium held in 1997, new concept of soliton transmission based on dispersion management of optical fibers were presented. This new soliton is now called the dispersion managed soliton. The p...
Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers
Chen, Baoqin; Hong, Lihong; Hu, Chenyang; Zhang, Chao; Liu, Rongjuan; Li, Zhiyuan
2018-03-01
Nonlinear frequency conversion offers an effective way to extend the laser wavelength range. Quadratic nonlinear photonic crystals (NPCs) are artificial materials composed of domain-inversion structures whose sign of nonlinear coefficients are modulated with desire to implement quasi-phase matching (QPM) required for nonlinear frequency conversion. These structures can offer various reciprocal lattice vectors (RLVs) to compensate the phase-mismatching during the quadratic nonlinear optical processes, including second-harmonic generation (SHG), sum-frequency generation and the cascaded third-harmonic generation (THG). The modulation pattern of the nonlinear coefficients is flexible, which can be one-dimensional or two-dimensional (2D), be periodic, quasi-periodic, aperiodic, chirped, or super-periodic. As a result, these NPCs offer very flexible QPM scheme to satisfy various nonlinear optics and laser frequency conversion problems via design of the modulation patterns and RLV spectra. In particular, we introduce the electric poling technique for fabricating QPM structures, a simple effective nonlinear coefficient model for efficiently and precisely evaluating the performance of QPM structures, the concept of super-QPM and super-periodically poled lithium niobate for finely tuning nonlinear optical interactions, the design of 2D ellipse QPM NPC structures enabling continuous tunability of SHG in a broad bandwidth by simply changing the transport direction of pump light, and chirped QPM structures that exhibit broadband RLVs and allow for simultaneous radiation of broadband SHG, THG, HHG and thus coherent white laser from a single crystal. All these technical, theoretical, and physical studies on QPM NPCs can help to gain a deeper insight on the mechanisms, approaches, and routes for flexibly controlling the interaction of lasers with various QPM NPCs for high-efficiency frequency conversion and creation of novel lasers.
Solitons on H bonds in proteins
DEFF Research Database (Denmark)
d'Ovidio, F.; Bohr, H.G.; Lindgård, Per-Anker
2003-01-01
system shows that the solitons are spontaneously created and are stable and moving along the helix axis. A perturbation on one of the three H-bond lines forms solitons on the other H bonds as well. The robust solitary wave may explain very long-lived modes in the frequency range of 100 cm(-1) which...... are found in recent x-ray laser experiments. The dynamics parameters of the Toda lattice are in accordance with the usual Lennard-Jones parameters used for realistic H-bond potentials in proteins....
Non-Abelian sine-Gordon solitons
Directory of Open Access Journals (Sweden)
Muneto Nitta
2015-06-01
Full Text Available We point out that non-Abelian sine-Gordon solitons stably exist in the U(N chiral Lagrangian. They also exist in a U(N gauge theory with two N by N complex scalar fields coupled to each other. One non-Abelian sine-Gordon soliton can terminate on one non-Abelian global vortex. They are relevant in chiral Lagrangian of QCD or in color-flavor locked phase of high density QCD, where the anomaly is suppressed at asymptotically high temperature or density, respectively.
Soliton excitations in Josephson tunnel junctions
DEFF Research Database (Denmark)
Lomdahl, P. S.; Sørensen, O. H.; Christiansen, Peter Leth
1982-01-01
A detailed numerical study of a sine-Gordon model of the Josephson tunnel junction is compared with experimental measurements on junctions with different L / λJ ratios. The soliton picture is found to apply well on both relatively long (L / λJ=6) and intermediate (L / λJ=2) junctions. We find good...... agreement for the current-voltage characteristics, power output, and for the shape and height of the zero-field steps (ZFS). Two distinct modes of soliton oscillations are observed: (i) a bunched or congealed mode giving rise to the fundamental frequency f1 on all ZFS's and (ii) a "symmetric" mode which...
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.
Nontopological solitons from functional integrals. II
International Nuclear Information System (INIS)
Cahill, R.T.; Williams, A.G.
1983-01-01
We demonstrate a general method for obtaining nontopological solitons from the functional-integral representation of Green's functions. We stress that these solitons arise in a most natural way from examining the properties of Green's functions, and we do not need to introduce any chemical potentials to act as Lagrange multipliers as was previously the case. We illustrate our method using a scalar field interacting with a set of fermion fields and show that we obtain equations identical to those obtained by the chemical-potential technique
Dissipative dark soliton in a complex plasma.
Heidemann, R; Zhdanov, S; Sütterlin, R; Thomas, H M; Morfill, G E
2009-04-03
The observation of a dark soliton in a three-dimensional complex plasma containing monodisperse microparticles is presented. We perform our experiments using neon gas in the bulk plasma of an rf discharge. A gas temperature gradient of 500K/m is applied to balance gravity and to levitate the particles in the bulk plasma. The wave is excited by a short voltage pulse on the electrodes of the radio frequency discharge chamber. It is found that the wave propagates with constant speed. The propagation time of the dark soliton is approximately 20 times longer than the damping time.
A CART extention using Quadratic Decision Borders
DEFF Research Database (Denmark)
Hartelius, Karsten
1999-01-01
In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature-space into subs......In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...
Heredity in one-dimensional quadratic maps
Romera, M.; Pastor, G.; Alvarez, G.; Montoya, F.
1998-12-01
In an iterative process, as is the case of a one-dimensional quadratic map, heredity has never been mentioned. In this paper we show that the pattern of a superstable orbit of a one-dimensional quadratic map can be expressed as the sum of the gene of the chaotic band where the pattern is to be found, and the ancestral path that joins all its ancestors. The ancestral path holds all the needed genetic information to calculate the descendants of the pattern. The ancestral path and successive descendant generations of the pattern constitute the family tree of the pattern, which is important to study and understand the orbit's ordering.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2003-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
On orthogonality preserving quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Reaction diffusion equations and quadratic convergence
Directory of Open Access Journals (Sweden)
A. S. Vatsala
1997-01-01
Full Text Available In this paper, the method of generalized quasilinearization has been extended to reaction diffusion equations. The extension includes earlier known results as special cases. The earlier results developed are when (i the right-hand side function is the sum of a convex and concave function, and (ii the right-hand function can be made convex by adding a convex function. In our present result, if the monotone iterates are mildly nonlinear, we establish the quadratic convergence as in the quasilinearization method. If the iterates are totally linear then the iterates converge semi-quadratically.
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Mechanisms of cascade collapse
International Nuclear Information System (INIS)
Diaz de la Rubia, T.; Smalinskas, K.; Averback, R.S.; Robertson, I.M.; Hseih, H.; Benedek, R.
1988-12-01
The spontaneous collapse of energetic displacement cascades in metals into vacancy dislocation loops has been investigated by molecular dynamics (MD) computer simulation and transmission electron microscopy (TEM). Simulations of 5 keV recoil events in Cu and Ni provide the following scenario of cascade collapse: atoms are ejected from the central region of the cascade by replacement collision sequences; the central region subsequently melts; vacancies are driven to the center of the cascade during resolidification where they may collapse into loops. Whether or not collapse occurs depends critically on the melting temperature of the metal and the energy density and total energy in the cascade. Results of TEM are presented in support of this mechanism. 14 refs., 4 figs., 1 tab
Analytical multi-soliton solutions of a (2+1)-dimensional breaking soliton equation.
Wang, Shao-Fu
2016-01-01
The analytical solutions for a (2+1)-dimensional breaking solution equation is proposed in this paper by using mapping and projective method darboux transformation, and Some exact propagating solutions are constructed for this Breaking equation, and the M × N multi-soliton could be obtained by using Weierstrassp function and setting the perfect parameters. The potential application of breaking Soliton equation will be of great interest in future research.
Multiple-μJ mid-IR supercontinuum generation in quadratic nonlinear crystals
DEFF Research Database (Denmark)
Bache, Morten; Zhou, Binbin; Ashihara, S.
2016-01-01
Pumping a quadratic nonlinear crystal in the mid-IR we observe octave-spanning mid-IR supercontinua. A self-acting cascaded process leads to the formation of a self-defocusing nonlinearity, allowing formation of filament-free octave-spanning supercontinua in the 2.0–7.0 μm range with 10s of μJ pu......J pulse energies, much higher than filament-based techniques. This allows to use the supercontinuum as ultra-broadband excitation pulses in nonlinear optical applications....
Solitons and spin transport in graphene boundary
Indian Academy of Sciences (India)
Solitons and spin transport in graphene boundary. KUMAR ABHINAV1, VIVEK M VYAS2 and PRASANTA K PANIGRAHI1,∗. 1Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur 741 246, India. 2Institute of Mathematical Sciences, Tharamani, Chennai 600 113, India. ∗Corresponding author.
Novel energy sharing collisions of multicomponent solitons
Indian Academy of Sciences (India)
2015-10-21
Oct 21, 2015 ... In this paper, we discuss the fascinating energy sharing collisions of multicomponent solitons in certain incoherently coupled and coherently coupled ... Post Graduate and Research Department of Physics, Bishop Heber College, Tiruchirappalli 620 017, India; Department of Physics, Anna University, ...
Infrared Absorption in Acetanilide by Solitons
DEFF Research Database (Denmark)
Careri, G.; Buontempo, U.; Carta, F.
1983-01-01
The infrared spectrum of acetanilide shows a new band that is red shifted from the main amide-I maximum by about 15 cm-1, the intensity of which increases at low temperature. It is suggested that this band may arise from the creation of amide-I solitons that are similar (but not identical) to those...
soliton dynamics in a modified Yakushevich model
Indian Academy of Sciences (India)
1Department of Physics, College of Engineering and Technology, Biju Patnaik University of Technology, Bhubaneswar 751 ... senting different bases and find two new in-phase solitonic solutions. We also discuss here the effect of ..... (29) and adoption of the procedure of linear perturbation anal- ysis [13-15] gives. ШШ =.
One-soliton solutions from Laplace's seed
Indian Academy of Sciences (India)
One-soliton solutions of axially symmetric vacuum Einstein ﬁeld equations are presented in this paper. Two sets of Laplace's solutions are used as seed and it is shown that the derived solutions reduce to some already known solutions when the constants are properly adjusted. An analysis of the solutions in terms of the ...
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...
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)
soliton dynamics in a modified Yakushevich model
Indian Academy of Sciences (India)
1Department of Physics, College of Engineering and Technology, Biju Patnaik University of Technology, Bhubaneswar 751 003, India. 2College of Basic Science and Humanities, Orissa University of ..... which represents soliton translation. substitution in eq. (29) and adoption of the procedure of linear perturbation anal-.
Novel energy sharing collisions of multicomponent solitons
Indian Academy of Sciences (India)
In this paper, we discuss the fascinating energy sharing collisions of multicompo- nent solitons in certain incoherently coupled and coherently coupled nonlinear Schrödinger-type equations arising in the context of nonlinear optics. Keywords. Coupled nonlinear Schrödinger equations; Hirota's bilinearization method; bright.
Solitons and spin transport in graphene boundary
Indian Academy of Sciences (India)
2015-10-16
Oct 16, 2015 ... It is shown that in (2+1)-dimensional condensed matter systems, induced gravitational Chern–Simons (CS) action can play a crucial role for coherent spin transport in a finite geometry, provided zero-curvature condition is satisfied on the boundary. The role of the resultant KdV solitons is explicated. The fact ...
Novel energy sharing collisions of multicomponent solitons
Indian Academy of Sciences (India)
(say S2) experiences an opposite kind of energy switching due to the conservation law. ∫ ∞. −∞ |qj |2dt = constant,j = 1, 2. For the standard elastic collision property ascribed to the scalar solitons to occur here we need the magnitudes of the transition intensities to be unity which is possible for the specific choice (α. (1). 1 /α.
Formation of multiple dark photovoltaic spatial solitons
Indian Academy of Sciences (India)
We theoretically study the formation of multiple dark photovoltaic soliton splitting in the quasi-steady-state and steady-state regimes under open-circuit conditions. We ﬁnd that the initial width of the dark notch at the entrance face of the crystal is a key parameter for generating an even (or odd) number sequence of dark ...
Formation of multiple dark photovoltaic spatial solitons
Indian Academy of Sciences (India)
Abstract. We theoretically study the formation of multiple dark photovoltaic soliton splitting in the quasi-steady-state and steady-state regimes under open-circuit conditions. We find that the initial width of the dark notch at the entrance face of the crystal is a key parameter for generating an even (or odd) number sequence of ...
Solitons in Bose–Einstein condensates
Indian Academy of Sciences (India)
The solution (8) shows that both the density profile ρ(z) and the phase profile φ(z) travel with the same speed ... always travel with different speeds, contrary to the solitons of the repulsive GPE, where they travel with the ... tory using standing waves of laser light, load BEC atoms on such lattices, and also tune the interactions ...
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)
One-soliton solutions from Laplace's seed
Indian Academy of Sciences (India)
Abstract. One-soliton solutions of axially symmetric vacuum Einstein field equations are pre- sented in this paper. Two sets of Laplace's solutions are used as seed and it is shown that the derived solutions reduce to some already known solutions when the constants are properly adjusted. An analysis of the solutions in ...
Quantization of bag-like solitons
International Nuclear Information System (INIS)
Breit, J.D.
1982-01-01
The method of collective coordinates is used to quantize bag-like solitons formed by scalar and spinor fields. This method leads to approximate wave functions for quarks in the bag that are orthogonal to the translational modes. Solutions are given for the MIT bag limit of the fields. (orig.)
Fuzzy Stability of Quadratic Functional Equations
Directory of Open Access Journals (Sweden)
Jang Sun-Young
2010-01-01
Full Text Available The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations and in fuzzy Banach spaces.
A Practical Approach to Quadratic Equations.
Light, Peter
1983-01-01
The usual methods for solving quadratic equations are noted to require either the use of numerical formula or curve plotting on graph paper. The method described here enables pupils to solve equations using only a 45 degree setsquare, graph paper, and a pencil for those which have both real roots and real coefficients. (Author/MP)
Fuzzy Stability of Quadratic Functional Equations
Dong Yun Shin; Choonkil Park; Sun-Young Jang; Jung Rye Lee
2010-01-01
The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations and in fuzzy Banach spaces.
Modulational instability in periodic quadratic nonlinear materials
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...
Target manifold formation using a quadratic SDF
Hester, Charles F.; Risko, Kelly K. D.
2013-05-01
Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.
Quadratic independence of coordinate functions of certain ...
Indian Academy of Sciences (India)
It is indeed a very important and interesting problem in the theory of quantum groups and noncommutative geometry ... independence of the algebra of natural coordinate functions on a large class of homoge- neous spaces of a .... Quadratic independence and nonexistence of genuine quantum group action. Let V be a finite ...
Investigating Students' Mathematical Difficulties with Quadratic Equations
O'Connor, Bronwyn Reid; Norton, Stephen
2016-01-01
This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…
STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY
Directory of Open Access Journals (Sweden)
Damián Fernández
2014-12-01
Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.
Shozo, TAKENO; Department of Physics, Kyoto Technical University
1982-01-01
It is shown that for the two-and three-dimensional sine-Gordon equations there exist exact multi-(resonant-soliton)-soliton solutions and vortex-like solutions, in addition to exact multi-soliton and resonant-soliton solutions.
Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients
Directory of Open Access Journals (Sweden)
Xue-Gang Zhou
2014-01-01
Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.
The quasi-line soliton: Solutions to the Davey-Stewartson I equation
Arai, Takahito
2012-01-01
[Abstract] A periodic soliton is turned into a line soliton accordingly as a parameter point approaches to the boundary of the existing domain in the parameter space for a non-singular periodic soliton solution. We will call the periodic soliton solution with parameters of the neighborhood of the boundary a quasi-line soliton in this paper. We will examine that a periodic soliton turn into the line soliton as the parameter point of a periodic soliton approaches to the neighborhood of the boun...
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Zhou, Binbin
2011-01-01
When ultrafast noncritical cascaded second-harmonic generation of energetic femtosecond pulses occur in a bulk lithium niobate crystal optical Cherenkov waves are formed in the near- to mid-IR. Numerical simulations show that the few-cycle solitons radiate Cherenkov (dispersive) waves in the λ = ...... efficiency is up to 25%. Thus, optical Cherenkov waves formed with cascaded nonlinearities could become an efficient source of energetic near- to mid-IR few-cycle pulses.......When ultrafast noncritical cascaded second-harmonic generation of energetic femtosecond pulses occur in a bulk lithium niobate crystal optical Cherenkov waves are formed in the near- to mid-IR. Numerical simulations show that the few-cycle solitons radiate Cherenkov (dispersive) waves in the λ = 2...
Radiation by solitons due to higher-order dispersion
DEFF Research Database (Denmark)
Karpman, V.I.
1993-01-01
We consider the Korteweg-de Vries (KdV) and nonlinear Schrodinger (NS) equations with higher-order derivative terms describing dispersive corrections. Conditions of existence of stationary and radiating solitons of the fifth-order KdV equation are obtained. An asymptotic time-dependent solution...... to the latter equation, describing the soliton radiation, is found. The radiation train may be in front as well as behind the soliton, depending on the sign of dispersion. The change rate of the soliton due to the radiation is calculated. A modification of the WKB method, that permits one to describe...... in a simple and general way the radiation of KdV and NS, as well as other types. of solitons, is developed. From the WKB approach it follows that the soliton radiation is a result of a tunneling transformation of the non-linearly self-trapped wave into the free-propagating radiation....
Experiments on soliton motion in annular Josephson junctions
DEFF Research Database (Denmark)
Davidson, A.; Dueholm, B.; Pedersen, Niels Falsig
1986-01-01
We report here the results of an extensive experimental investigation of soliton dynamics in Josephson junctions of different annular geometries. The annular geometry is unique in that it allows for the study of undisturbed soliton motion as well as soliton–antisoliton collisons, since...... there are no boundary effects. We have successfully trapped a single soliton in an annular junction and found good agreement with perturbation theory at low soliton velocity, and evidence of departure from perturbation theory at higher velocity. We also discuss the observation of fine structure on the I-V curve...... for a single trapped soliton, and evidence linking the stability of the soliton to surface damping. Journal of Applied Physics is copyrighted by The American Institute of Physics....
3 GHz, watt-level femtosecond Raman soliton source.
Lim, Jinkang; Chen, Hung-Wen; Xu, Shanhui; Yang, Zhongmin; Chang, Guoqing; Kärtner, Franz X
2014-04-01
We demonstrate a 3 GHz repetition rate, femtosecond Raman soliton source with its wavelength tunable from 1.15 to 1.35 μm. We investigate the dependence of Raman soliton formation on different photonic-crystal fibers (PCFs), input powers, and fiber lengths. To produce a Raman soliton peaking at the same wavelength, shorter PCFs demand higher input average powers and consequently generate stronger Raman soliton pulses. Using 30 cm PCF NL-3.2-945, the resulting Raman soliton pulse at 1.35 μm has 0.9 W average power. The integrated relative intensity noise of the Raman soliton pulse at 1.35 μm generated from the 54-cm PCF NL-3.2-945 is as low as 0.33% from 100 Hz to 10 MHz.
Modulation instability and solitons in two-color nematic crystals
Energy Technology Data Exchange (ETDEWEB)
Horikis, Theodoros P., E-mail: horikis@uoi.gr
2016-10-14
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic liquid crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis reveals that while the nonlocal term suppresses the growth rates, substantially, the coupled system exhibits significantly higher growth rates than its scalar counterpart. In the soliton case, the necessary conditions are derived that lead the solitons to exhibit stable, undistorted evolution, suppressing any breathing behavior and radiation, leading to soliton mutual guiding. - Highlights: • Modulation instability analysis for two-color nematic crystals. • Stable soliton propagation for two-color nematic crystals. • Conditions for stable propagation of continuous waves and solitons in two-color nematic crystals.
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
Wang, Jian-Bo; Reetz, Manfred T.
2015-12-01
Racemic or enantiomerically pure alcohols can be converted with high yield into enantiopure chiral amines in a one-pot redox-neutral cascade process by the clever combination of an alcohol dehydrogenase and an appropriate amine dehydrogenase.
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....
Learning optimal embedded cascades.
Saberian, Mohammad Javad; Vasconcelos, Nuno
2012-10-01
The problem of automatic and optimal design of embedded object detector cascades is considered. Two main challenges are identified: optimization of the cascade configuration and optimization of individual cascade stages, so as to achieve the best tradeoff between classification accuracy and speed, under a detection rate constraint. Two novel boosting algorithms are proposed to address these problems. The first, RCBoost, formulates boosting as a constrained optimization problem which is solved with a barrier penalty method. The constraint is the target detection rate, which is met at all iterations of the boosting process. This enables the design of embedded cascades of known configuration without extensive cross validation or heuristics. The second, ECBoost, searches over cascade configurations to achieve the optimal tradeoff between classification risk and speed. The two algorithms are combined into an overall boosting procedure, RCECBoost, which optimizes both the cascade configuration and its stages under a detection rate constraint, in a fully automated manner. Extensive experiments in face, car, pedestrian, and panda detection show that the resulting detectors achieve an accuracy versus speed tradeoff superior to those of previous methods.
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
International Nuclear Information System (INIS)
Serkin, Vladimir N; Belyaeva, T L
2001-01-01
The existence of the Lax representation for a model of soliton management under certain conditions is shown, which proves a complete integrability of the model. The exact analytic solutions are obtained for the problem of the optimal control of parameters of Schrodinger solitons in nonconservative systems with the group velocity dispersion, nonlinear refractive index, and gain (absorption coefficient) varying over the length. The examples demonstrating the non-trivial amplification dynamics of optical solitons, which are important from practical point of view, are considered. The exact analytic solutions are obtained for problems of the optimal amplification of solitons in optical fibres with monotonically decreasing dispersion and of Raman pumping of solitons in fibreoptic communication systems. (solitons)
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
On the theory of ultracold neutrons scattering by Davydov solitons
International Nuclear Information System (INIS)
Brizhik, L.S.
1984-01-01
Elastic coherent scattering of ultracold neutrons by Davydov solitons in one-dimensional periodic molecular chains without account of thermal oscillations of chain atoms is studied. It is shown that the expression for the differential cross section of the elastic neutron scattering by Davydov soliton breaks down into two components. One of them corresponds to scattering by a resting soliton, the other is proportional to the soliton velocity and has a sharp maximum in the direction of mirror reflection of neutrons from the chain
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 soliton-based functionalities in complementary metal-oxide-semiconductor-compatible platforms. PMID:24423977
Soliton formation in hollow-core photonic bandgap fibers
DEFF Research Database (Denmark)
Lægsgaard, Jesper
2009-01-01
The formation of solitons upon compression of linearly chirped pulses in hollow-core photonic bandgap fibers is investigated numerically. The dependence of soliton duration on the chirp and power of the input pulse and on the dispersion slope of the fiber is investigated, and the validity...... of an approximate scaling relation is tested. It is concluded that compression of input pulses of several ps duration and sub-MW peak power can lead to a formation of solitons with ∼100 fs duration and multi-megawatt peak powers. The dispersion slope of realistic hollow-core fibers appears to be the main obstacle...... for forming still shorter solitons...
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.
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.
Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons.
Veretenov, N A; Fedorov, S V; Rosanov, N N
2017-12-29
We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., N_{c} knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M_{0} (N_{c}, M, and M_{0} are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines N_{c}=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M=1, 2, and 3.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda......-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2003-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda......-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda......-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...
Quaternion orders, quadratic forms, and Shimura curves
Alsina, Montserrat
2004-01-01
Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
International Nuclear Information System (INIS)
Yan Zhenya; Hang Chao
2009-01-01
We provide analytical three-dimensional bright multisoliton solutions to the (3+1)-dimensional Gross-Pitaevskii equation with time- and space-dependent potential, time-dependent nonlinearity, and gain or loss. The zigzag propagation trace and the breathing behavior of solitons are observed. Different shapes of bright solitons and fascinating interactions between two solitons can be achieved with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.
Quadratic Term Structure Models in Discrete Time
Marco Realdon
2006-01-01
This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...
Stochastic Linear Quadratic Optimal Control Problems
International Nuclear Information System (INIS)
Chen, S.; Yong, J.
2001-01-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well
Applications: Quadratic Formulas Up to NCTM's Curriculum Standards.
Nievergelt, Yves
1992-01-01
Discusses an alternative form of the quadratic formula to solve quadratic equations. Presents an application to chemistry to illustrate the need for quadratic formulas better suited to approximations obtained using hand-held calculators. Addresses the problems of rounding errors, accuracy of solutions, and factoring as a method of solution. (MDH)
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...
Graphical Solution of the Monic Quadratic Equation with Complex Coefficients
Laine, A. D.
2015-01-01
There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…
Estimating quadratic variation using realized variance
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Shephard, N.
2002-01-01
This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process is a semimar......This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process...... is a semimartingale we recall the fundamental result that RV is a consistent (as M ) estimator of quadratic variation (QV). We express concern that without additional assumptions it seems difficult to give any measure of uncertainty of the RV in this context. The position dramatically changes when we work...... with a rather general SV model - which is a special case of the semimartingale model. Then QV is integrated variance and we can derive the asymptotic distribution of the RV and its rate of convergence. These results do not require us to specify a model for either the drift or volatility functions, although we...
Quadratic tracer dynamical models tobacco growth
International Nuclear Information System (INIS)
Qiang Jiyi; Hua Cuncai; Wang Shaohua
2011-01-01
In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)
Quadratic sinusoidal analysis of voltage clamped neurons.
Magnani, Christophe; Moore, Lee E
2011-11-01
Nonlinear biophysical properties of individual neurons are known to play a major role in the nervous system, especially those active at subthreshold membrane potentials that integrate synaptic inputs during action potential initiation. Previous electrophysiological studies have made use of a piecewise linear characterization of voltage clamped neurons, which consists of a sequence of linear admittances computed at different voltage levels. In this paper, a fundamentally new theory is developed in two stages. First, analytical equations are derived for a multi-sinusoidal voltage clamp of a Hodgkin-Huxley type model to reveal the quadratic response at the ionic channel level. Second, the resulting behavior is generalized to a novel Hermitian neural operator, which uses an algebraic formulation capturing the entire quadratic behavior of a voltage clamped neuron. In addition, this operator can also be used for a nonlinear identification analysis directly applicable to experimental measurements. In this case, a Hermitian matrix of interactions is built with paired frequency probing measurements performed at specific harmonic and interactive output frequencies. More importantly, eigenanalysis of the neural operator provides a concise signature of the voltage dependent conductances determined by their particular distribution on the dendritic and somatic membrane regions of neurons. Finally, the theory is concretely illustrated by an analysis of an experimentally measured vestibular neuron, providing a remarkably compact description of the quadratic responses involved in the nonlinear processing underlying the control of eye position during head rotation, namely the neural integrator.
Topological solitons in the supersymmetric Skyrme model
Energy Technology Data Exchange (ETDEWEB)
Gudnason, Sven Bjarke [Institute of Modern Physics, Chinese Academy of Sciences,Lanzhou 730000 (China); Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences,Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan); Sasaki, Shin [Department of Physics, Kitasato University,Sagamihara 252-0373 (Japan)
2017-01-04
A supersymmetric extension of the Skyrme model was obtained recently, which consists of only the Skyrme term in the Nambu-Goldstone (pion) sector complemented by the same number of quasi-Nambu-Goldstone bosons. Scherk-Schwarz dimensional reduction yields a kinetic term in three or lower dimensions and a potential term in two dimensions, preserving supersymmetry. Euclidean solitons (instantons) are constructed in the supersymmetric Skyrme model. In four dimensions, the soliton is an instanton first found by Speight. Scherk-Schwarz dimensional reduction is then performed once to get a 3-dimensional theory in which a 3d Skyrmion-instanton is found and then once more to get a 2d theory in which a 2d vortex-instanton is obtained. Although the last one is a global vortex it has finite action in contrast to conventional theory. All of them are non-BPS states breaking all supersymmetries.
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
Soliton dual frequency combs in crystalline microresonators.
Pavlov, N G; Lihachev, G; Koptyaev, S; Lucas, E; Karpov, M; Kondratiev, N M; Bilenko, I A; Kippenberg, T J; Gorodetsky, M L
2017-02-01
We present a novel compact dual-comb source based on a monolithic optical crystalline MgF2 multi-resonator stack. The coherent soliton combs generated in the two microresonators of the stack with the repetition rate of 12.1 GHz and difference of 1.62 MHz provided after heterodyning a 300 MHz wide radio frequency comb. An analogous system can be used for dual-comb spectroscopy, coherent LIDAR applications, and massively parallel optical communications.
Schlenker, Cody W.
2011-09-27
We demonstrate planar organic solar cells consisting of a series of complementary donor materials with cascading exciton energies, incorporated in the following structure: glass/indium-tin-oxide/donor cascade/C 60/bathocuproine/Al. Using a tetracene layer grown in a descending energy cascade on 5,6-diphenyl-tetracene and capped with 5,6,11,12-tetraphenyl- tetracene, where the accessibility of the π-system in each material is expected to influence the rate of parasitic carrier leakage and charge recombination at the donor/acceptor interface, we observe an increase in open circuit voltage (Voc) of approximately 40% (corresponding to a change of +200 mV) compared to that of a single tetracene donor. Little change is observed in other parameters such as fill factor and short circuit current density (FF = 0.50 ± 0.02 and Jsc = 2.55 ± 0.23 mA/cm2) compared to those of the control tetracene-C60 solar cells (FF = 0.54 ± 0.02 and Jsc = 2.86 ± 0.23 mA/cm2). We demonstrate that this cascade architecture is effective in reducing losses due to polaron pair recombination at donor-acceptor interfaces, while enhancing spectral coverage, resulting in a substantial increase in the power conversion efficiency for cascade organic photovoltaic cells compared to tetracene and pentacene based devices with a single donor layer. © 2011 American Chemical Society.
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
Hadron cascades produced by electromagnetic cascades
International Nuclear Information System (INIS)
Nelson, W.R.; Jenkins, T.M.; Ranft, J.
1986-12-01
A method for calculating high energy hadron cascades induced by multi-GeV electron and photon beams is described. Using the EGS4 computer program, high energy photons in the EM shower are allowed to interact hadronically according to the vector meson dominance (VMD) model, facilitated by a Monte Carlo version of the dual multistring fragmentation model which is used in the hadron cascade code FLUKA. The results of this calculation compare very favorably with experimental data on hadron production in photon-proton collisions and on the hadron production by electron beams on targets (i.e., yields in secondary particle beam lines). Electron beam induced hadron star density contours are also presented and are compared with those produced by proton beams. This FLUKA-EGS4 coupling technique could find use in the design of secondary beams, in the determination high energy hadron source terms for shielding purposes, and in the estimation of induced radioactivity in targets, collimators and beam dumps
Euler potentials for the MHD Kamchatnov-Hopf soliton solution
Semenov, VS; Korovinski, DB; Biernat, HK
2002-01-01
In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf
Phase conjugation of gap solitons: A numerical study
Indian Academy of Sciences (India)
studies reporting gap soliton-induced all-optical switching with large contrast [8]. All opti- cal logic operations using coupled gap solitons have also been reported [9]. Very recently, ..... Government of India for financial support. MR would like to acknowledge a fellowship from Council of Scientific and Industrial Research, ...
Protocol of networks using energy sharing collisions of bright solitons
Indian Academy of Sciences (India)
two components is conserved in the latter. In this paper, we consider the dynamics of two solitons of integrable two-component. CNLS equations of both Manakov and mixed types, which are placed on the primary star graph (PSG) in figure 1. We shall show how the nature of PSG will change through two-soliton collisions.
Bunched soliton states in weakly coupled sine-Gordon systems
DEFF Research Database (Denmark)
Grønbech-Jensen, N.; Samuelsen, Mogens Rugholm; Lomdahl, P. S.
1990-01-01
The interaction between solitons of two weakly coupled sine-Gordon systems is considered. In particular, the stability of bunched states is investigated, and perturbation results are compared with numerical results.......The interaction between solitons of two weakly coupled sine-Gordon systems is considered. In particular, the stability of bunched states is investigated, and perturbation results are compared with numerical results....
Soliton-based ultra-high speed optical communications
Indian Academy of Sciences (India)
evolution of information and introduction of optical soliton solution as the stable nonlinear solution. The paper ... aged solitons will be presented to demonstrate the effectiveness of dispersion management techniques both .... Most high speed transmission systems at present use an all optical scheme with loss compensated ...
Bistable soliton states and switching in doubly inhomogeneously ...
Indian Academy of Sciences (India)
there has been a considerable interest in bistable solitons in glass fibers (with non-Kerr properties), in connection with optical bistability and other possible applications leading to switching and logic-gate devices. In literature one distinguishes between two kinds of bistable solitons: one for which the nonlinear propagation ...
Solitons and their interactions in classical field theory
International Nuclear Information System (INIS)
Belova, T.I.; Kudryavtsev, A.E.
1997-01-01
Effects of nonlinearity in the classical field theory for non-integrated systems are considered, such as soliton scattering, soliton bound states, the fractal nature of resonant structures, kink scattering by inhomogeneities, and domain bladder collapse. The results are presented in both (1 + 1) and higher dimensions. Both neutral and charged scalar fields are considered. Possible applications areas for the nonlinearity effects are discussed
Reality conditions of loop solitons genus $g$: hyperelliptic am functions
Directory of Open Access Journals (Sweden)
Shigeki Matsutani
2007-06-01
Full Text Available This article is devoted to an investigation of a reality condition of a hyperelliptic loop soliton of higher genus. In the investigation, we have a natural extension of Jacobi am-function for an elliptic curves to that for a hyperelliptic curve. We also compute winding numbers of loop solitons.
Twisted topological solitons and dislocations in a polymer crystal
DEFF Research Database (Denmark)
Savin, A. V.; Khalack, J. M.; Christiansen, Peter Leth
2002-01-01
of adjacent molecular chains in the polymer crystal). It is shown that some of these defects called "twisted topological solitons" can propagate with a stationary profile and velocity. To describe the dynamics of these solitons, a model that accounts for the three components of the molecular displacements...
Bright and dark soliton solutions of the (3+ 1)-dimensional ...
Indian Academy of Sciences (India)
In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sech p and tanh p functions, we obtain exact analytical bright and dark soliton solutions for the considered ...
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 80; Issue 2. Soliton solutions of some nonlinear evolution equations with time-dependent coefficients ... In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable ...
Bistable soliton states and switching in doubly inhomogeneously ...
Indian Academy of Sciences (India)
Dec. 2001 physics pp. 969–979. Bistable soliton states and switching in doubly inhomogeneously doped fiber couplers. AJIT KUMAR. Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110 016, India. Abstract. Switching between the bistable soliton states in a doubly and inhomogeneously doped.
Chaotic behaviour from smooth and non-smooth optical solitons ...
Indian Academy of Sciences (India)
2016-07-14
Jul 14, 2016 ... obtain the preferable media to reduce the influ- ence of perturbation of solitons in optical fibre propagation. This paper is organized as follows. In §2, we give the smooth and compacton solitons of the perturbation system by phase diagram analysis. In §3, we discuss the chaotic behaviour of the perturbed ...
Ion-acoustic solitons in multispecies spatially inhomogeneous ...
Indian Academy of Sciences (India)
Ion-acoustic solitons are investigated in the spatially inhomogeneous plasma having electrons-positrons and ions. The soliton characteristics are described by Korteweg-de Vries equation which has an additional term. The density and temperature of different species play an important role for the amplitude and width of the ...
Dynamics of solitons in multicomponent long wave–short wave ...
Indian Academy of Sciences (India)
Abstract. In this paper, we study the formation of solitons, their propagation and collision behaviour in an integrable multicomponent (2+1)-dimensional long wave–short wave resonance interaction (M-LSRI) system. First, we briefly revisit the earlier results on the dynamics of bright solitons and demonstrate the fascinating ...
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 ...
Nucleon-antinucleon annihilation in chiral soliton model
International Nuclear Information System (INIS)
Musakhanov, M.M.; Tashkentskij Gosudarstvennyj Univ., Tashkent; Musatov, I.V.
1991-01-01
We investigate annihilation process of nucleons in the chiral soliton model by the path integral method. A soliton-antisoliton pair is shown to decay into mesons at range of about 1fm, defined by the S bar S potential. Contribution of the annihilation channel to the elastic scattering is discussed
Ion-acoustic solitons in multispecies spatially inhomogeneous ...
Indian Academy of Sciences (India)
Abstract. Ion-acoustic solitons are investigated in the spatially inhomogeneous plasma having electrons–positrons and ions. The soliton characteristics are described by. Korteweg–de Vries equation which has an additional term. The density and temperature of different species play an important role for the amplitude and ...
Bore-Soliton-Splash: van spektakel naar oceaangolf
Bokhove, Onno; Gagarina, Elena; Zweers, Wout; Thornton, Anthony Richard
2011-01-01
Ons nieuwe universiteitsplein heeft een magnifieke golfgoot (figuur 1). Door drie professoren afzonderlijk was ons midden september 2010 gevraagd om een soliton te maken in deze goot om het plein feestelijk te openen. Een soliton is een enkelvoudige golf, een gelokaliseerde opéénhoping van zich snel
Influence of soliton distributions on the spin-dependent electronic ...
Indian Academy of Sciences (India)
In this paper, a detailed numerical study of the role of selected soliton distributions on the spin-dependent ... Based on Su–. Schrieffer–Heeger (SSH) Hamiltonian and using a generalized Green's function formalism, we ... walls or solitons, which appear to be responsible for many of the remarkable properties of trans-PA ...
Some aspects of optical spatial solitons in photorefractive media and ...
Indian Academy of Sciences (India)
2015-10-22
Oct 22, 2015 ... Mechanisms of formation of screening and photovoltaic solitons of three different configurations, i.e., bright, dark and grey varieties have been examined. Incoherently coupled vector solitons due to single and two-photon photorefractive phenomena have been highlighted. Modulation instability of a broad ...
Potential motion for Thomas-Fermi non-topological solitons
International Nuclear Information System (INIS)
Bahcall, S.
1992-04-01
In the Thomas-Fermi approximation to theories of coupled fermions and scalars, the equations for spherically-symmetric non-topological solitons have the form of potential motion. This gives a straightforward method for proving the existence of non-topological solitons in a given theory and for finding the constant-density, saturating solutions
Dynamics of coupled field solitons: A collective coordinate approach
Indian Academy of Sciences (India)
mensional space-time, with the main motivation of studying classical stability of soliton solutions using collective coordinate ... presented in some previous works [1,2] which where motivated by investigations intro- duced in [3,4], ... The collision of coupled field solitons leads to resonance structure depending on the energy ...
Integrable coupling system of fractional soliton equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-10-05
In this Letter, we consider the derivatives and integrals of fractional order and present a class of the integrable coupling system of the fractional order soliton equations. The fractional order coupled Boussinesq and KdV equations are the special cases of this class. Furthermore, the fractional AKNS soliton equation hierarchy is obtained.
Soliton-based ultra-high speed optical communications
Indian Academy of Sciences (India)
Dispersion management techniques are then introduced as a means to overcome these prob- lems and description of nonlinear pulse (the dispersion managed soliton) in a dispersion managed fiber is presented. Examples of recent remarkable experimental results of transmission of dispersion man- aged solitons will be ...
Interaction between "dissipative solitons" stabilized by aggregation in excitable kinetics
Mangioni, Sergio E.
2014-10-01
We consider that a population of individuals governed by the Nagumo model is characterized by predisposition towards aggregation. "Dissipative solitons" interacting are solutions for such system. We changed the possibility of extinction, predicted by Nagumo model, by a uniform background of low population's density and then we observed relevant effect on interaction between "solitons".
Lin, Wei; Wang, Simin; Xu, Shanhui; Luo, Zhi-Chao; Yang, Zhongmin
2015-06-01
A combined analytical approach to classify soliton dynamics from dissipative soliton to dissipative soliton resonance (DSR) is developed based on the established laser models. The approach, derived from two compatible analytical solutions to the complex cubic-quintic Ginzburg-Landau equation (CQGLE), characterizes the pulse evolution process from both algebraic and physical points of view. The proposed theory is proved to be valid in real world laser oscillators according to numerical simulations, and potentially offers guideline on the design of DSR cavity configurations.
Dynamics of soliton explosions in ultrafast fiber lasers at normal-dispersion.
Du, Yueqing; Shu, Xuewen
2018-03-05
We found two kinds of soliton explosions based on the complex Ginzburg-Landau equation without nonlinearity saturation and high-order effects, demonstrating the soliton explosions as an intrinsic property of the dissipative systems. The two kinds of soliton explosions are caused by the dual-pulsing instability and soliton erupting, respectively. The transformation and relationship between the two kinds of soliton explosions are discussed. The parameter space for the soliton explosion in a mode-locked laser cavity is found numerically. Our results can help one to obtain or avoid the soliton explosions in mode-locked fiber lasers and understand the nonlinear dynamics of the dissipative systems.
Asymmetric soliton mobility in competing linear-nonlinear parity-time-symmetric lattices.
Kartashov, Yaroslav V; Vysloukh, Victor A; Torner, Lluis
2016-09-15
We address the transverse mobility of spatial solitons in competing parity-time-symmetric linear and nonlinear lattices. The competition between out-of-phase linear and nonlinear lattices results in a drastic mobility enhancement within a range of soliton energies. We show that within such a range, the addition of even a small imaginary part in the linear potential makes soliton mobility strongly asymmetric. For a given initial phase tilt, the velocity of soliton motion grows with an increase of the balanced gain/losses. In this regime of enhanced mobility, tilted solitons can efficiently drag other solitons that were initially at rest to form moving soliton pairs.
Collective Modes of a Soliton Train in a Fermi Superfluid.
Dutta, Shovan; Mueller, Erich J
2017-06-30
We characterize the collective modes of a soliton train in a quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In addition to the expected Goldstone and Higgs modes, we find novel long-lived gapped modes associated with oscillations of the soliton cores. The soliton train has an instability that depends strongly on the interaction strength and the spacing of solitons. It can be stabilized by filling each soliton with an unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We find that such a state is always dynamically stable, which paves the way for realizing long-lived FFLO states in experiments via phase imprinting.
Soliton repetition rate in a silicon-nitride microresonator.
Bao, Chengying; Xuan, Yi; Wang, Cong; Jaramillo-Villegas, Jose A; Leaird, Daniel E; Qi, Minghao; Weiner, Andrew M
2017-02-15
The repetition rate of a Kerr comb composed of a single soliton in an anomalous group velocity dispersion silicon-nitride microcavity is measured as a function of pump frequency. By comparing operation in the soliton and non-soliton states, the contributions from the Raman soliton self-frequency shift (SSFS) and the thermal effects are evaluated; the SSFS is found to dominate the changes in the repetition rate, similar to silica cavities. The relationship between the changes in the repetition rate and the pump frequency detuning is found to be independent of the nonlinearity coefficient and dispersion of the cavity. Modeling of the repetition rate change by using the generalized Lugiato-Lefever equation is discussed; the Kerr shock is found to have only a minor effect on repetition rate for cavity solitons with duration down to ∼50 fs.
Soliton-induced relativistic-scattering and amplification
Rubino, E.; Lotti, A.; Belgiorno, F.; Cacciatori, S. L.; Couairon, A.; Leonhardt, U.; Faccio, D.
2012-01-01
Solitons are of fundamental importance in photonics due to applications in optical data transmission and also as a tool for investigating novel phenomena ranging from light generation at new frequencies and wave-trapping to rogue waves. Solitons are also moving scatterers: they generate refractive index perturbations moving at the speed of light. Here we found that such perturbations scatter light in an unusual way: they amplify light by the mixing of positive and negative frequencies, as we describe using a first Born approximation and numerical simulations. The simplest scenario in which these effects may be observed is within the initial stages of optical soliton propagation: a steep shock front develops that may efficiently scatter a second, weaker probe pulse into relatively intense positive and negative frequency modes with amplification at the expense of the soliton. Our results show a novel all-optical amplification scheme that relies on soliton induced scattering. PMID:23226830
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
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.
Edge-soliton-mediated vortex-core reversal dynamics.
Lee, Ki-Suk; Yoo, Myoung-Woo; Choi, Youn-Seok; Kim, Sang-Koog
2011-04-08
We report an additional reversal mechanism of magnetic vortex cores in nanodot elements driven by currents flowing perpendicular to the sample plane, occurring via dynamic transformations between two coupled edge solitons and bulk vortex solitons. This mechanism differs completely from the well-known switching process mediated by the creation and annihilation of vortex-antivortex pairs in terms of the associated topological solitons, energies, and spin-wave emissions. Strongly localized out-of-plane gyrotropic fields induced by the fast motion of the coupled edge solitons enable a magnetization dip that plays a crucial role in the formation of the reversed core magnetization. This work provides a deeper physical insight into the dynamic transformations of magnetic topological solitons in nanoelements.
Optimal Asset Allocation under Quadratic Loss Aversion
Fortin, Ines; Hlouskova, Jaroslava
2012-01-01
Abstract: We study the asset allocation of a quadratic loss-averse (QLA) investor and derive conditions under which the QLA problem is equivalent to the mean-variance (MV) and conditional value-at-risk (CVaR) problems. Then we solve analytically thetwo-asset problem of the QLA investor for a risk-free and a risky asset. We find that the optimal QLA investment in the risky asset is finite, strictly positive and is minimal with respect to the reference point for a value strictly larger than the...
Quadratic stochastic operators: Results and open problems
International Nuclear Information System (INIS)
Ganikhodzhaev, R.N.; Rozikov, U.A.
2009-03-01
The history of the quadratic stochastic operators can be traced back to the work of S. Bernshtein (1924). For more than 80 years this theory has been developed and many papers were published. In recent years it has again become of interest in connection with numerous applications in many branches of mathematics, biology and physics. But most results of the theory were published in non English journals, full text of which are not accessible. In this paper we give a brief description of the results and discuss several open problems. (author)
Vector nature of multi-soliton patterns in a passively mode-locked figure-eight fiber laser.
Ning, Qiu-Yi; Liu, Hao; Zheng, Xu-Wu; Yu, Wei; Luo, Ai-Ping; Huang, Xu-Guang; Luo, Zhi-Chao; Xu, Wen-Cheng; Xu, Shan-Hui; Yang, Zhong-Min
2014-05-19
The vector nature of multi-soliton dynamic patterns was investigated in a passively mode-locked figure-eight fiber laser based on the nonlinear amplifying loop mirror (NALM). By properly adjusting the cavity parameters such as the pump power level and intra-cavity polarization controllers (PCs), in addition to the fundamental vector soliton, various vector multi-soliton regimes were observed, such as the random static distribution of vector multiple solitons, vector soliton cluster, vector soliton flow, and the state of vector multiple solitons occupying the whole cavity. Both the polarization-locked vector solitons (PLVSs) and the polarization-rotating vector solitons (PRVSs) were observed for fundamental soliton and each type of multi-soliton patterns. The obtained results further reveal the fundamental physics of multi-soliton patterns and demonstrate that the figure-eight fiber lasers are indeed a good platform for investigating the vector nature of different soliton types.
The wrinkle-like N-solitons for the thermophoretic motion equation through graphene sheets
Ma, Yu-Lan; Li, Bang-Qing
2018-03-01
The main work is focused on the thermophoretic motion equation, which was derived from wrinkle wave motions in substrate-supported graphene sheets. Via the bilinear method, a class of wrinkle-like N-soliton solutions is constructed. The one-soliton, two-soliton and three-soliton are observed graphically. The shape, amplitude, open direction and width of the N-solitons are controllable through certain parameters.
N-Soliton Solutions of the Nonisospectral Generalized Sawada-Kotera Equation
Directory of Open Access Journals (Sweden)
Jian Zhou
2014-01-01
Full Text Available The soliton interaction is investigated based on solving the nonisospectral generalized Sawada-Kotera (GSK equation. By using Hirota method, the analytic one-, two-, three-, and N-soliton solutions of this model are obtained. According to those solutions, the relevant properties and features of line-soliton and bright-soliton are illustrated. The results of this paper will be useful to the study of soliton resonance in the inhomogeneous media.
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2004-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...
Soliton interactions and complexes for coupled nonlinear Schrödinger equations.
Jiang, Yan; Tian, Bo; Liu, Wen-Jun; Sun, Kun; Li, Min; Wang, Pan
2012-03-01
Under investigation in this paper are the coupled nonlinear Schrödinger (CNLS) equations, which can be used to govern the optical-soliton propagation and interaction in such optical media as the multimode fibers, fiber arrays, and birefringent fibers. By taking the 3-CNLS equations as an example for the N-CNLS ones (N≥3), we derive the analytic mixed-type two- and three-soliton solutions in more general forms than those obtained in the previous studies with the Hirota method and symbolic computation. With the choice of parameters for those soliton solutions, soliton interactions and complexes are investigated through the asymptotic and graphic analysis. Soliton interactions and complexes with the bound dark solitons in a mode or two modes are observed, including that (i) the two bright solitons display the breatherlike structures while the two dark ones stay parallel, (ii) the two bright and dark solitons all stay parallel, and (iii) the states of the bound solitons change from the breatherlike structures to the parallel one even with the distance between those solitons smaller than that before the interaction with the regular one soliton. Asymptotic analysis is also used to investigate the elastic and inelastic interactions between the bound solitons and the regular one soliton. Furthermore, some discussions are extended to the N-CNLS equations (N>3). Our results might be helpful in such applications as the soliton switch, optical computing, and soliton amplification in the nonlinear optics.
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.
Quadratic residues and non-residues selected topics
Wright, Steve
2016-01-01
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
Integrable Abelian vortex-like solitons
Directory of Open Access Journals (Sweden)
Felipe Contatto
2017-05-01
Full Text Available We propose a modified version of the Ginzburg–Landau energy functional admitting static solitons and determine all the Painlevé-integrable cases of its Bogomolny equations of a given class of models. Explicit solutions are determined in terms of the third Painlevé transcendents, allowing us to calculate physical quantities such as the vortex number and the vortex strength. These solutions can be interpreted as the usual Abelian-Higgs vortices on surfaces of non-constant curvature with conical singularity.
Ramanujan's identities, minimal surfaces and solitons
Indian Academy of Sciences (India)
In this paper, using some of Ramanujan's identites and the W–E representation of minimal surfaces, and the analogue for B–I solitons, we obtain non-trivial identities. (1) For ζ = ±1, ±i and belonging to a suitable domain in C,. Re ln. (. 1 + ζ2. 1 − ζ2. ) = ∞. ∑ k=1 ln. ⎛. ⎝. −Im ln. (. 1+ζ. 1−ζ. ) −. ( k − 1. 2. ) π. 2 Re tan−1(ζ ) −.
ON IMMERSION FORMULAS FOR SOLITON SURFACES
Directory of Open Access Journals (Sweden)
Alfred Michel Grundland
2016-06-01
Full Text Available This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the linear spectral problem, conformal transformations in the spectral parameter and generalized symmetries of the associated integrable system. After a brief exposition of the theory of soliton surfaces and of the main tool used to study classical and generalized Lie symmetries, we derive the necessary and sufficient conditions under which the immersion formulas associated with these symmetries are linked by gauge transformations. We illustrate the theoretical results by examples involving the sigma model.
On the theory of Langmuir solitons
International Nuclear Information System (INIS)
Gibbons, J.; Thornhill, S.G.; Wardrop, M.J.; Ter Haar, D.
1977-01-01
A Lagrangian density is found from which the equations of motion for the Langmuir solitons follow in the usual way. It is shown how this Lagrangian leads to the usual conservation laws. For the one-dimensional case a consideration of these conservation laws can help in understanding some of the results obtained in numerical experiments on the behaviour of a strongly turbulent plasma. It is shown that the situation in the three-dimensional case may be fundamentally different, and the near-sonic perturbations and Karpman's treatment of these is discussed. (U.K.)
Integrable Abelian vortex-like solitons
Energy Technology Data Exchange (ETDEWEB)
Contatto, Felipe, E-mail: felipe.contatto@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); CAPES Foundation, Ministry of Education of Brazil, Brasília, DF 70040-020 (Brazil)
2017-05-10
We propose a modified version of the Ginzburg–Landau energy functional admitting static solitons and determine all the Painlevé-integrable cases of its Bogomolny equations of a given class of models. Explicit solutions are determined in terms of the third Painlevé transcendents, allowing us to calculate physical quantities such as the vortex number and the vortex strength. These solutions can be interpreted as the usual Abelian-Higgs vortices on surfaces of non-constant curvature with conical singularity.
Solitonic Integrable Perturbations of Parafermionic Theories
Fernández-Pousa, C R; Hollowood, Timothy J; Miramontes, J L
1997-01-01
The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.
Quadratic forms and Clifford algebras on derived stacks
Vezzosi, Gabriele
2013-01-01
In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We define the associated notion of derived Clifford algebra, in all these contexts, and compare it with its classical version, when they both apply. Finally, we prove three main existence results for derived shifted quadratic forms over derived stacks, define ...
Dragging two-dimensional discrete solitons by moving linear defects.
Brazhnyi, Valeriy A; Malomed, Boris A
2011-07-01
We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear Schrödinger lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in a uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a localized mode pinned by the Peierls-Nabarro potential, irrespective of the initial velocity. However, the soliton attached to the moving defect can be dragged over an indefinitely long distance (including routes with abrupt turns and circular trajectories) virtually without losses, provided that the dragging velocity is smaller than a certain critical value. Collisions between solitons dragged by two defects in opposite directions are studied too. If the velocity is small enough, the collision leads to a spontaneous symmetry breaking, featuring fusion of two solitons into a single one, which remains attached to either of the two defects.
Steller Structure Treatment of Quadratic Gravity
Chen, Y.; Shao, C.; Chen, X.
2001-07-01
A scheme for considering stellar structure by taking advantage of the quadratic theory of gravitation in four-dimensions is proposed, citing the fact that the possible deviation of gravity in astrophysical systems from the Newtonian inverse square law can be explained through the use of this theory. A modified Lane-Emden equation is derived by making use of the linearized static field equation of quadratic gravity and the polytropic equation of state for a fluid. The influence on stellar structure of the additional force included in quadratic gravity is investigated. It is shown that the additional force can be treated as a perturbation of a bound system by solutions of the modified Lane-Emden equation and an order-of-magnitude analysis. %ZY. Fujii, Nature (London) 234 (1971), 5; Phys. Rev. D9 (1974), 874. D. R. Long, Phys. Rev. D 9 (1974), 850. J. O'Hanlon, Phys. Rev. Lett. 29 (1972), 137. D. R. Mikkelson and M. J. Newman, Phys. Rev. D 16 (1977), 919. R. V. Wagoner, Phys. Rev. D 1 (1970), 3209. J. Z. Xu and Y. H. Chen, Gen. Relat. Gravit. J. 23 (1991), 169. K. S. Stelle, Gen. Relat. Gravit. J. 8 (1978), 631. C. Xu and G. F. R. Ellis, Class. Quant. Grav. 8 (1991), 1747. A. Eddington, The Mathematical Theory of Relativity, 2nd ed. (Cambridge University Press, Cambridge, 1924). W. Pauli, Theory of Relativity (Pergamon Press, New York, 1921). H. A. Buchdahl, Proc. Edinburgh Math. Soc. 8 (1948), 89. J. D. Barrow and A. C. Ottewill, J. of Phys. A 16 (1983), 2757. M. B. Mijic, M. S. Morris and W. M. Suen, Phys. Rev. D 34 (1986), 2934. A. L. Berkin, Phys. Rev. D 42 (1990), 1017. N. D. Birrell and P. C. W. Davies, Quantum Field in Curved Space (Cambridge University Press, 1982). E. T. Tomboulis, Quantum Theory of Gravity, ed. S. M. Christensen (Bristol: Adam Hilger 1984). H. J. Treder, Ann. der Phys. 32 (1975), 383. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York 1972). E. N. Glass and G. Szamosi
On Coupled Rate Equations with Quadratic Nonlinearities
Montroll, Elliott W.
1972-01-01
Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013
Gain scheduled linear quadratic control for quadcopter
Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.
2017-12-01
This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.
Quadratic dynamical decoupling with nonuniform error suppression
International Nuclear Information System (INIS)
Quiroz, Gregory; Lidar, Daniel A.
2011-01-01
We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N 1 and N 2 pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N 1 and N 2 , and near-optimal performance is achieved for general single-qubit interactions when N 1 =N 2 .
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which......Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... is due to Johnsson. This search is carried out by a transitive closure. Instead, we partition the call graph of the source program into strongly connected components, based on the simple observation that all functions in each component need the same extra parameters and thus a transitive cl osure...
Quadratic gravity in first order formalism
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Enrique; Anero, Jesus; Gonzalez-Martin, Sergio, E-mail: enrique.alvarez@uam.es, E-mail: jesusanero@gmail.com, E-mail: sergio.gonzalez.martin@uam.es [Departamento de Física Teórica and Instituto de Física Teórica (IFT-UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid (Spain)
2017-10-01
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than 1/ p {sup 2}. The drawback is of course that the parameter space of the theory is too big, so that in many cases will be far away from a theory of gravity alone. In order to analyze this issue, the interaction between external sources was examined in some detail. We find that this interaction is conveyed mainly by propagation of the three-index connection field. At any rate the theory as it stands is in the conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated by quantum corrections.
Low-rank quadratic semidefinite programming
Yuan, Ganzhao
2013-04-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Large-scale sequential quadratic programming algorithms
Energy Technology Data Exchange (ETDEWEB)
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
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
The Baryon Number Two System in the Chiral Soliton Model
International Nuclear Information System (INIS)
Mantovani-Sarti, V.; Drago, A.; Vento, V.; Park, B.-Y.
2013-01-01
We study the interaction between two B = 1 states in a chiral soliton model where baryons are described as non-topological solitons. By using the hedgehog solution for the B = 1 states we construct three possible B = 2 configurations to analyze the role of the relative orientation of the hedgehog quills in the dynamics. The strong dependence of the inter soliton interaction on these relative orientations reveals that studies of dense hadronic matter using this model should take into account their implications. (author)
Ring resonator systems to perform optical communication enhancement using soliton
Amiri, Iraj Sadegh
2014-01-01
The title explain new technique of secured and high capacity optical communication signals generation by using the micro and nano ring resonators. The pulses are known as soliton pulses which are more secured due to having the properties of chaotic and dark soliton signals with ultra short bandwidth. They have high capacity due to the fact that ring resonators are able to generate pulses in the form of solitons in multiples and train form. These pulses generated by ring resonators are suitable in optical communication due to use the compact and integrated rings system, easy to control, flexibi
Peaked and Smooth Solitons for K*(4,1 Equation
Directory of Open Access Journals (Sweden)
Yongan Xie
2013-01-01
Full Text Available This paper is contributed to explore all possible single peak solutions for the K*(4,1 equation ut=uxu2+2α(uuxxx+2uxuxx. Our procedure shows that the K*(4,1 equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal limξ→±∞u=A≠0 or possesses compacton solutions only when limξ→±∞u=A=0. We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the K*(4,1 equation.
Theory of nonlocal soliton interaction in nematic liquid crystals
DEFF Research Database (Denmark)
Rasmussen, Per Dalgaard; Bang, Ole; Krolikowski, Wieslaw
2005-01-01
We investigate interactions between spatial nonlocal bright solitons in nematic liquid crystals using an analytical “effective particle” approach as well as direct numerical simulations. The model predicts attraction of out-of-phase solitons and the existence of their stable bound state....... This nontrivial property is solely due to the nonlocal nature of the nonlinear response of the liquid crystals. We further predict and verify numerically the critical outwards angle and degree of nonlocality which determine the transition between attraction and repulsion of out-of-phase solitons....
Classification of the line-soliton solutions of KPII
Chakravarty, Sarbarish; Kodama, Yuji
2008-07-01
In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| → ∞. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.
Optical image processing by using a photorefractive spatial soliton waveguide
Energy Technology Data Exchange (ETDEWEB)
Liang, Bao-Lai, E-mail: liangbaolai@gmail.com [College of Physics Science & Technology, Hebei University, Baoding 071002 (China); Wang, Ying; Zhang, Su-Heng; Guo, Qing-Lin; Wang, Shu-Fang; Fu, Guang-Sheng [College of Physics Science & Technology, Hebei University, Baoding 071002 (China); Simmonds, Paul J. [Department of Physics and Micron School of Materials Science & Engineering, Boise State University, Boise, ID 83725 (United States); Wang, Zhao-Qi [Institute of Modern Optics, Nankai University, Tianjin 300071 (China)
2017-04-04
By combining the photorefractive spatial soliton waveguide of a Ce:SBN crystal with a coherent 4-f system we are able to manipulate the spatial frequencies of an input optical image to perform edge-enhancement and direct component enhancement operations. Theoretical analysis of this optical image processor is presented to interpret the experimental observations. This work provides an approach for optical image processing by using photorefractive spatial solitons. - Highlights: • A coherent 4-f system with the spatial soliton waveguide as spatial frequency filter. • Manipulate the spatial frequencies of an input optical image. • Achieve edge-enhancement and direct component enhancement operations of an optical image.
Soliton solutions for some x-dependent nonlinear evolution equations
International Nuclear Information System (INIS)
Wang, Pan
2014-01-01
Under investigation in this paper are two x-dependent nonlinear evolution equations: the generalized x-dependent nonlinear Schrödinger (NLS) equation and the modified Korteweg–de Vries (KdV) equation. With the help of Hirota method and symbolic computation, the one- and two-soliton solutions have been obtained for the generalized x-dependent NLS and KdV equations. Propagation and evolution of one soliton have been investigated through the physical quantities of amplitude, width and velocity. The effects of the parameters in the equations on the interaction of two solitons have been studied analytically and graphically. (paper)
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.
Baryons as non-topological chiral solitons
Christov, Chr. V.; Blotz, A.; Kim, H.-C.; Pobylitsa, P.; Watabe, T.; Meissner, Th.; Ruiz Arriola, E.; Goeke, K.
The present review gives a survey of recent developments and applications of the Nambu-Jona-Lasinio model with Nf = 2 and Nf = 3 quark flavors for the structure of baryons. The model is an effective chiral quark theory which incorporates the SU(N f) L⊗SU(N f) R⊗U(1) V approximate symmetry of Quantum chromodynamics. The approach describes the spontaneous chiral symmetry breaking and dynamical quark mass generation. Mesons appear as quark-antiquark excitations and baryons arise as non-topological solitons with three valence quarks and a polarized Dirac sea. For the evaluation of the baryon properties the present review concentrates on the non-linear Nambu-Jona-Lasinio model with quark and Goldstone degrees of freedom which is identical to the Chiral quark soliton model obtained from the instanton liquid model of the QCD vacuum. In this non-linear model, a wide variety of observables of baryons of the octet and decuplet is considered. These include, in particular, electromagnetic, axial, pseudoscalar and pion nucleon form factors and the related static properties like magnetic moments, radii and coupling constants of the nucleon as well as the mass splittings and electromagnetic form factors of hyperons. Predictions are given for the strange form factors, the scalar form factor and the tensor charge of the nucleon.
Solitonic Josephson-based meminductive systems.
Guarcello, Claudio; Solinas, Paolo; Di Ventra, Massimiliano; Giazotto, Francesco
2017-04-24
Memristors, memcapacitors, and meminductors represent an innovative generation of circuit elements whose properties depend on the state and history of the system. The hysteretic behavior of one of their constituent variables, is their distinctive fingerprint. This feature endows them with the ability to store and process information on the same physical location, a property that is expected to benefit many applications ranging from unconventional computing to adaptive electronics to robotics. Therefore, it is important to find appropriate memory elements that combine a wide range of memory states, long memory retention times, and protection against unavoidable noise. Although several physical systems belong to the general class of memelements, few of them combine these important physical features in a single component. Here, we demonstrate theoretically a superconducting memory based on solitonic long Josephson junctions. Moreover, since solitons are at the core of its operation, this system provides an intrinsic topological protection against external perturbations. We show that the Josephson critical current behaves hysteretically as an external magnetic field is properly swept. Accordingly, long Josephson junctions can be used as multi-state memories, with a controllable number of available states, and in other emerging areas such as memcomputing, i.e., computing directly in/by the memory.
International Nuclear Information System (INIS)
Diaz-Otero, Francisco J.; Guillán-Lorenzo, Omar; Pedrosa-Rodríguez, Laura
2017-01-01
Highlights: • Empirical model describing the pulse energy enhancement required to obtain stable pulses to higher-order polynomial equations • An improvement in the accuracy is obtained through the addition of a new quartic addend dependent on the map strength. • This conclusion is validated through a comparison in a commercial DM soliton submarine network. • The error in the interaction distance for two adjacent pulses in the same channel is of the same order as the energy error - Abstract: We study the propagation properties of nonlinear pulses with periodic evolution in a dispersion-managed transmission link by means of a variational approach. We fit the energy enhancement required for stable propagation of a single soliton in a prototypical commercial link to a polynomial approximation that describes the dependence of the energy on the map strength of the normalized unit cell. We present an improvement of a relatively old and essential result, namely, the dependence of the energy-enhancement factor of dispersion-management solitons with the square of the map strength of the fiber link. We find that adding additional corrections to the conventional quadratic formula up to the fourth order results in an improvement in the accuracy of the description of the numerical results obtained with the variational approximation. Even a small error in the energy is found to introduce large deviations in the pulse parameters during its evolution. The error in the evaluation of the interaction distance between two adjacent time division multiplexed pulses propagating in the same channel in a prototypical submarine link is of the same order as the error in the energy.
Ion-sound emission by Langmuir soliton reflected at density barrier
International Nuclear Information System (INIS)
El-Ashry, M.Y.
1989-07-01
The emission of ion-sound waves by an accelerated Langmuir soliton is studied. The acceleration of the soliton is due to an inhomogeneous density barrier. On the assumption that the kinetic energy of the Langmuir soliton is smaller than the potential energy created by the barrier. The basic equations describing the dynamic behaviour of the soliton and the emission of the ion-sound waves are formulated. The qualitative spatial distributions of the perturbed concentration in the ion-sound waves are analyzed at different characteristic points of the soliton. The energy lost by the soliton, as a result of the emission, is estimated. (author). 6 refs, 4 figs
Dark and bright solitons in a quasi-one-dimensional Bose-Einstein condensate
International Nuclear Information System (INIS)
Wang, Shun-Jin; Jia, Cheng-Long; An, Jun-Hong; Zhao, Dun; Luo, Hong-Gang
2003-01-01
The analytical dark and bright soliton solutions of the one-dimensional Gross-Pitaevskii equation with a confining potential are obtained. For the bright soliton, the recent experimental finding is studied, and the particle number of the soliton and the window of the particle numbers for the bright soliton to occur are estimated analytically and in good agreement with the experimental data. The existence of dark soliton for the attractive interaction and bright soliton for the repulsive interaction is predicted under proper conditions
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
2016-01-01
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain. PMID:27596716
Three-Dimensional Hermite—Bessel—Gaussian Soliton Clusters in Strongly Nonlocal Media
International Nuclear Information System (INIS)
Jin Hai-Qin; Yi Lin; Liang Jian-Chu; Cai Ze-Bin; Liu Fei
2012-01-01
We analytically and numerically demonstrate the existence of Hermite—Bessel—Gaussian spatial soliton clusters in three-dimensional strongly nonlocal media. It is found that the soliton clusters display the vortex, dipole azimuthon and quadrupole azimuthon in geometry, and the total number of solitons in the necklaces depends on the quantum number n and m of the Hermite functions and generalized Bessel polynomials. The numerical simulation is basically identical to the analytical solution, and white noise does not lead to collapse of the soliton, which confirms the stability of the soliton waves. The theoretical predictions may give new insights into low-energetic spatial soliton transmission with high fidelity
Existence of solutions of some quadratic integral equations
Directory of Open Access Journals (Sweden)
Giuseppe Anichini
2008-01-01
Full Text Available In this paper we study the existence of continuous solutions of quadratic integral equations. The theory of quadratic integral equations has many useful applications in mathematical physics, economics, biology, as well as in describing real world problems. The main tool used in our investigations is a fixed point result for the multivalued solution's map with acyclic values.
Decentralized linear quadratic power system stabilizers for multi ...
Indian Academy of Sciences (India)
Power system stabilizer; linear quadratic regulator; small-signal stability; transient stability. Abstract. Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state ...
Orthogonal and Scaling Transformations of Quadratic Functions with ...
African Journals Online (AJOL)
In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...
Binary GCD like Algorithms for Some Complex Quadratic Rings
DEFF Research Database (Denmark)
Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg
2004-01-01
binary gcd like algorithms for the ring of integers in and , one now has binary gcd like algorithms for all complex quadratic Euclidean domains. The running time of our algorithms is O(n 2) in each ring. While there exists an O(n 2) algorithm for computing the gcd in quadratic number rings by Erich...
Quadratic Twists of Rigid Calabi–Yau Threefolds Over
DEFF Research Database (Denmark)
Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko
2013-01-01
of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...
orthogonal and scaling transformations of quadratic functions with ...
African Journals Online (AJOL)
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ABSTRACT: In this paper we present a non-singular transformation that can reduce a given quadratic function defined on n. R to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that ...