Interaction of oblique dark solitons in two-dimensional supersonic nonlinear Schrödinger flow

We investigate the collision of two oblique dark solitons in the two-dimensional supersonic nonlinear Schrödinger flow past two impenetrable obstacles. We numerically show that this collision is very similar to the dark solitons collision in the one-dimensional case. We observe that it is practically elastic and we measure the shifts of the solitons positions after their interaction.     

Fractal structure in the collision of vector solitons

We study the collision of two orthogonally polarized and equal-amplitude vector solitons in the nonintegrable coupled nonlinear Schrodinger equations. We show that the separation velocity versus collision velocity graph has a fractal structure. When we zoom into this graph, we get a structure qualitatively identical to the original one. In addition, collision dynamics in the zoomed-in windows is intimately related to that in the original graph. We explain this fractal dependence of the collision by a resonance mechanism between the translational motion of vector solitons and internal oscillations inside a vector soliton.     

Solitons,Bäcklund transformation and Lax pair for a variable-coefficient generalized Boussinesq system in the shallow water

Under investigation in this paper is a variable-coefficient generalized Boussinesq system, which describes the propagation of long weakly non-linear and weakly dispersive surface waves in the shallow water. Bilinear form, Bäcklund transformation and Lax pair are derived by virtue of the Bell polynomials. One- and two-soliton solutions are constructed via the Hirota method. Propagation characteristics and collision behaviors of the solitons are discussed through the graphical analysis. Elastic collisions of the two bell- and periodic-shaped solitons are obtained. Head-on collision between the two solitons occurs when the sign of the two wave numbers are different; Otherwise, the overtaking collision happens.     

Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrödinger equations with focusing,defocusing and mixed type nonlinearities

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.     

相干光伏空间孤子非对称碰撞研究

采用数值方法研究了三个呈非对称分布的相干光伏空间孤子碰撞相互作用.结果表明,随着信号光的入射角度在一定范围内逐渐改变,三个孤子在晶体中碰撞后会产生孤子的分裂或湮没现象.当孤子碰撞后出现分裂或湮没时,若保持孤子的碰撞角度不变,改变其中任意一个孤子的初始相对相位,孤子的碰撞行为也将随之迅速改变,产生新的孤子分裂、湮没或其他碰撞现象.另外,研究结果还表明,作为具有不可积哈密顿系统特性的光伏孤子,其小角度碰撞过程中动量和能量仍然是守恒的. 关键词： 光伏孤子 非对称碰撞 分裂 湮没     

PARTICULAR SOLITONS IN NONLINEAR LATTICE

One soliton of particle velocity and its amplitude (maximum particle velocity of one soliton) in Toda lattice is given analytically. It has also been known numerically that the maximum particle velocity (when the collision of two solitons reaches their maximum, we define V_n at this time as its maximum particle velocity) during the collision of two solitons moving in the same direction is equal to the difference between the amplitudes of two solitons if the difference is large enough; however, the maximum particle velocity is equal to the adding up of the amplitudes of two solitons moving in the opposite directions. The relationship between the maximum value of e^-(r_n)-1 and their initial amplitude of e^-(r_n)-1 is also given analytically in Toda lattice if the amplitudes of the two solitons are the same and their moving directions are opposite. Compared with the Boussinesq equation, there are differences between the Toda lattice equation and the Boussinesq equation for solitons during the collision.     

Superposition solitons in two-component Bose-Einstein condensates

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.     

Vector kink-dark complex solitons in a three-component Bose–Einstein condensate

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.     

微扰变分法对光折变空间孤子相互作用的研究

利用微扰变分法研究了光折变屏蔽孤子的相干相互作用,得出了光折变空间屏蔽孤子在晶体中同相相互作用时发生第一次碰撞的位置和碰撞周期解析表达式,并对孤子同相和反相相互作用的物理机制进行了分析.研究结果表明:当两孤子尾部交叠时就会发生相互作用,相互作用力的大小与孤子的相对强度、相对间距以及晶体外加电场的大小有关.孤子的相对强度越大、相对间距越小以及晶体外加电场越强,孤子间相互作用力越大；相互作用力的性质与初始相位差有关,同相相互吸引,反相相互排斥.     

Davydov soliton collisions

In this Letter, we study the collisions of Davydov solitons. The collision behaviour is diverse and complicated, and very sensitive to both the initial phases and velocities of the solitons. For some parameter ranges, Davydov solitons are stable to collisions in the sense that the solitons retain their structures, though for some cases, the propagation direction may be altered. For other parameter ranges, significant structural changes may occur: An exchange of energy between solitons, or the merger of two solitons to form a new bound state.