General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.
General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.
复制标题
DOI：
10.1103/physreve.88.062921
复制
发表时间：
2013-12
期刊：
影响因子：
--
通讯作者：
T. Kanna;K. Sakkaravarthi;K. Tamilselvan
中科院分区：
文献类型：
--
作者：
T. Kanna;K. Sakkaravarthi;K. Tamilselvan
我们考虑多分量Yajima-Oikawa(YO)系统，证明了在三耦合非线性薛定谔(3-CNLS)型系统的物理背景下，用渐近约化方法可以得到两分量YO系统。并将其进一步推广到多组分情况。这组方程描述了一维长波和多个短波之间的非线性共振相互作用的动力学。对一般多分量YO系统的Painlevé分析表明，演化方程组对于任意的非线性系数是可积的，这将导致对应于正、负和混合非线性系数的三组不同的方程组。利用Hirota的双线性化方法，得到了Gram行列式形式的多元Yo系统的一般亮N-孤子解，并对上述三种非线性系数选择下的多元Yo系统的单孤子解和双孤子解进行了显式分析。我们还指出，当发生长波-短波共振时，3-CNLS系统存在亮、暗、反暗和灰色型的特殊渐近孤子。短波分量孤子经历两种类型的能量共享碰撞。具体地说，在两分量YO系统中，我们证明了两种类型的能量共享碰撞--(I)特定孤子在两个分量中性质相反的能量切换和(Ii)在两个分量中给定孤子的相似类型的能量切换--导致两种不同的非线性系数选择。长波分量中出现的孤子总是表现出弹性碰撞，而短波分量中的孤子只有在特定的参数选择下才表现出标准的弹性碰撞。我们还研究了原始3-CNLS系统中渐近孤子的碰撞动力学。为了完备性，我们探索了三孤子相互作用，证明了碰撞的成对性质，并揭示了令人着迷的态恢复性质。
We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.