共查询到20条相似文献,搜索用时 234 毫秒
1.
M. Vijayajayanthi T. Kanna M. Lakshmanan 《The European physical journal. Special topics》2009,173(1):57-80
Bright and bright-dark type multisoliton solutions of the integrable N-coupled nonlinear Schrödinger (CNLS) equations with focusing, defocusing and mixed type nonlinearities are obtained by using Hirota’s bilinearization method. Particularly, for the bright soliton case, we present the Gram type determinant form of the n-soliton solution (n:arbitrary) for both focusing and mixed type nonlinearities and explicitly prove that the determinant form indeed satisfies the corresponding bilinear equations. Based on this, we also write down the multisoliton form for the mixed (bright-dark) type solitons. For the focusing and mixed type nonlinearities with vanishing boundary conditions the pure bright solitons exhibit different kinds of nontrivial shape changing/energy sharing collisions characterized by intensity redistribution, amplitude dependent phase-shift and change in relative separation distances. Due to nonvanishing boundary conditions the mixed N-CNLS system can admit coupled bright-dark solitons. Here we show that the bright solitons exhibit nontrivial energy sharing collision only if they are spread up in two or more components, while the dark solitons appearing in the remaining components undergo mere standard elastic collisions. Energy sharing collisions lead to exciting applications such as collision based optical computing and soliton amplification. Finally, we briefly discuss the energy sharing collision properties of the solitons of the (2+1) dimensional long wave-short wave resonance interaction (LSRI) system. 相似文献
2.
S. V. Sazonov 《Journal of Experimental and Theoretical Physics》2006,103(1):126-140
An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations. 相似文献
3.
We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low. 相似文献
4.
In this paper, we construct the bright-soliton bound states of an integrable (2 + 1)-dimensional multicomponent long wave-short wave resonance interaction (LSRI) system by using the exact bright-soliton solutions obtained in Ref. [24] and analyze their interesting collision dynamics. We show that the beating and breathing oscillations of the bound solitons can be controlled by tuning the polarization parameters. Also, we explore the interaction between the bound-soliton and a standard soliton. We also point out that the two bound-soliton state seems to be robust against collision with a standard soliton and remain to be bounded even after collision. 相似文献
5.
6.
YANG Jian-Rong MAO Jie-Jian 《理论物理通讯》2008,49(1):22-26
With Hirota's bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift. 相似文献
7.
We investigate the soliton dynamics of the electromagnetic wave propagating in an inhomogeneous or deformed ferromagnet. The dynamics of magnetization and the propagation of electromagnetic waves are governed by the Landau–Lifshitz–Maxwell (LLM) equation, a certain coupling between the Landau–Lifshitz and Maxwell's equations. In the framework of multiscale analysis, we obtain the perturbed integral modified KdV (PIMKdV) equation. Since the dynamic is governed by the nonlinear integro-differential equation, we rely on numerical simulations to study the interaction of its mKdV solitons with various types of inhomogeneities. Apart from simple one soliton experiments with periodic or localised inhomogeneities, the numerical simulations revealed an interesting dynamical scenario where the collision of two solitons on a localised inhomogeneity create a bound state which then produces either two separated solitons or a mKdV breather. 相似文献
8.
E. M. Gromov L. V. Piskunova V. V. Tyutin 《Radiophysics and Quantum Electronics》1998,41(12):1051-1055
We present the results of numerical study of the evolution of wave packets and envelope soliton interaction in terms of the third-order nonlinear Schrödinger equation. It is shown that an arbitrary initial pulse evolves to a few solitons and a linear quasiperiodic wave. The interaction of solitons is accompanied by the radiation of part of the wave field in the form of a linear quasiperiodic wave from the interaction region, amplification of the soliton with larger amplitude and attenuation of the soliton with smaller amplitude. 相似文献
9.
By using a direct method, we construct the Hirota bilinear form for an extended (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation. Based on this bilinearization, the lump solitons and rogue wave solutions are investigated. Constraint conditions for the wave propagation and velocity for lump solitons are found and verified by figures. Also the lump-stripe interaction was investigated to show that the lump solitons will be swallowed by the stripe soliton. Finally, the dynamic behaviour for the obtained lump solution, rogue wave and lump-stripe soliton interaction by suitable special parameters is shown graphically. 相似文献
10.
Fusion and birth of spatial solitons upon collision 总被引:4,自引:0,他引:4
We study experimentally the collision of photorefractive screening solitons in a strontium barium niobate crystal. Depending on the relative phase of the solitons and their intersecting angle, such effects as soliton birth, energy exchange, and soliton fusion have been observed. 相似文献
11.
Min Li Bo Tian Wen-Jun Liu Yan Jiang Kun Sun 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2010,59(2):279-289
Coupled modified nonlinear Schr?dinger (CMNLS) equations
describe the pulse propagation in the picosecond or femtosecond
regime of the birefringent optical fibers. A new type of the Lax
pair and another hierarchy of the infinitely many conservation laws
are derived based on the Wadati-Konno-Ichikawa system. By means of
the Hirota method, soliton solutions in the normal dispersion regime
are obtained. Parametric regions for the existence of dark and
anti-dark vector soliton solutions are given. Asymptotic analysis
shows that the collision between two solitons (two anti-dark
solitons, two dark solitons, or dark and anti-dark solitons) in each
polarization direction is elastic. Moreover, there is no energy
transfer between two polarization components of each vector soliton,
whether dark or anti-dark vector soliton. In addition, dark and
anti-dark solitons can coexist on the same background seen from the
collision between the dark and anti-dark solitons in one
polarization direction. Our graphical analysis shows that the
parameters in the CMNLS equations not only determine the regions for
the existence of dark and anti-dark soliton solutions but also
control the phase and direction of the propagation of the solitons.
Finally, through the linear stability analysis, the modulational
instability condition is given. 相似文献
12.
D. Mihalache D. Mazilu F. Lederer 《The European physical journal. Special topics》2009,173(1):267-279
We report systematic results of collisions between discrete spatiotemporal Ginzburg-Landau solitons in waveguide arrays. Depending
on the value of the kick parameter (collision momentum), four generic outcomes are identified in the case of collision of
two identical solitons located at equal distances from the edge of the waveguide array: (a) merger of the solitons into a
single one, at small values of the kick parameter, (b) creation of an extra soliton at intermediate values of the collision
momentum, (c) quasi-elastic interactions at both intermediate values of the kick parameter (for relatively small values of
the cubic gain) and at large values of the kick parameter (for relatively high values of cubic gain), and (d) soliton spreading
at relatively large values of the collision momentum but only in the case of relatively small values of the cubic gain. In
the case of collision of two non-identical solitons located at different distances from the edge of the waveguide array four
generic outcomes were identified too: (e) soliton bouncing, accompanied by a sharp modification of soliton velocities during
the interaction process, for relatively small values of the collision momentum, (f) soliton creation at intermediate values
of the kick parameter and for relatively low values of the cubic gain, (g) soliton spreading (in time) at intermediate values
of the collision momentum and for relatively high values of the cubic gain, and (h) quasi-elastic interactions at large values
of the the kick parameter. 相似文献
13.
14.
We develop the Hirota bilinear method and obtain the exact one and two superposition soliton solutions for two-component Bose-Einstein condensates. The conversion of three kinds of solitons including the superposition solitons, bright-bright solitons, and dark-bright solitons is discussed. With the energy analysis, we find that the superposition soliton state is an excitation state for this system. Moreover, the collision of two superposition solitons is found to be elastic. 相似文献
15.
We investigate kink-dark complex solitons(KDCSs) in a three-component Bose–Einstein condensate(BEC) with repulsive interactions and pair-transition(PT) effects. Soliton profiles critically depend on the phase differences between dark solitons excitation elements. We report a type of kink-dark soliton profile which shows a droplet-bubble-droplet with a density dip, in sharp contrast to previously studied bubble-droplets. The interaction between two KDCSs is further investigated. It demonstrates some striking particle transition behaviours during their collision processes, while soliton profiles survive after the collision. Additionally, we exhibit the state transition dynamics between a kink soliton and a dark soliton. These results suggest that PT effects can induce more abundant complex solitons dynamics in multi-component BEC. 相似文献
16.
Merging and splitting dynamics between two bright solitons in dipolar Bose-Einstein condensates 下载免费PDF全文
We numerically study the interaction dynamics of two bright solitons with zero initial velocities in the one-dimensional dipolar Bose-Einstein condensates. Under different dipolar strengths, the two bright solitons can merge into a breathing wave, and then split or propagate constantly after several oscillating periods. We quantitatively study the breathing frequency of wave after merging and the asymmetry property of solitons after splitting, and analyze their formation mechanism by the system's energy evolution. Also, the change of initial phase difference brings distinct effects on the soliton interaction. Our results provide insight into the new dynamical phenomena in dipolar systems and enrich the understanding for interaction between dipolar solitons. 相似文献
17.
Luis A. Cisneros-Ake Hugo Parra Prado Diego Joselito López Villatoro R. Carretero-González 《Physics letters. A》2018,382(12):837-845
We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg–de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS–mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution. 相似文献
18.
O. E. Kurkina A. A. Kurkin E. A. Ruvinskaya E. N. Pelinovsky T. Soomere 《JETP Letters》2012,95(2):91-95
Nonlinear wave dynamics is discussed using the extended modified Korteweg-de Vries equation that includes the combination
of the third- and fifth-order terms and is valid for waves in a three-layer fluid with so-called symmetric stratification.
The derived equation has solutions in the form of solitary waves of various polarities. At small amplitudes, they are close
to solitons of the modified Korteweg-de Vries equation. However, the height of large-amplitude solutions has a limit approaching
which solitary waves widen and acquire a table like shape similar to soluitons of the Gardner equation. Numerical calculations
confirm that the collision of solitons of the derived equation is inelastic. Inelasticity is the most pronounced in the interaction
of unipolar pulses. The direction of the shift of the phase of the higher-amplitude soliton owing to the interaction of solitons
of different polarities depends on the amplitudes of the pulses. 相似文献
19.
In this paper, we present exact femtosecond one- and two-dark soliton solutions for a variable-coefficient higher-order nonlinear Schrödinger equation via modified Hirota method. The propagation and interaction of femtosecond dark solitons are investigated in inhomogeneous fiber systems. Elastic collision, bound oscillation and parallel propagation can be achieved in both Gaussian distributed parameter system and exponentially periodic distributed parameter system by choosing the appropriate distributed parameters and soliton parameters. The results may be beneficial to the realization of interaction control of femtosecond dark solitons in communication systems. 相似文献
20.
The dynamics of short (of the order of a few wave periods) intense optical pulses and interaction of short optical solitons in fibers are considered within the framework of the third-order nonlinear Schrodinger equation. It is shown that an initial pulse tends to one or a few short solitons plus a linear quasiperiodic wave when the third-order linear dispersion and nonlinear dispersion have parameters of the same sign. The number and parameters of the solitons depend on the magnitudes of initial pulse parameters. Interaction of short optical solitons having different amplitudes is accompanied by radiation of part of the wave field from the area of interaction, by an increase of the soliton with larger amplitude, and a decrease of the soliton with a smaller one. (c) 2000 American Institute of Physics. 相似文献