General Mixed Multi-Soliton Solutions to One-Dimensional Multicomponent Yajima-Oikawa System
General Mixed Multi-Soliton Solutions to One-Dimensional Multicomponent Yajima-Oikawa System
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DOI：
10.7566/jpsj.84.074001
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
Junchao Chen;Yong Chen;B. Feng;K. Maruno
中科院分区：
文献类型：
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作者：
Junchao Chen;Yong Chen;B. Feng;K. Maruno
本文针对一维多分量Yajima-Oikawa （YO）系统，即由M分量短波（SWs）和1分量长波（LW）组成的（M+1）分量YO系统，对所有可能的非线性系数组合（包括正、负和混合型），导出了一般混合（亮-暗）多孤子解。利用kp层次约简方法，我们首先详细构造了（3+1）组分YO体系的两类一般混合n孤子解（双亮一暗孤子和SW组分的一亮二暗孤子）。然后将相应的分析推广到（M+1）分量的YO系统，得到了一个Gram行列式的一般混合n孤子解。混合孤子溶液的表达式还包含一般的全亮和全暗n孤子溶液作为特例。此外，动力学分析表明，只有当混合孤子溶液中至少有两个SW分量具有亮孤子时，SW分量之间才会发生非弹性碰撞。而SW分量中的暗孤子和LW分量中的亮孤子总是发生通常的弹性碰撞。
In this paper, we derive a general mixed (bright-dark) multi-soliton solution to a one-dimensional multicomponent Yajima-Oikawa (YO) system, i.e., the (M+1)-component YO system comprised of M-component short waves (SWs) and one-component long wave (LW) for all possible combinations of nonlinearity coefficients including positive, negative and mixed types. With the help of the KP-hierarchy reduction method, we firstly construct two types of general mixed N-soliton solution (two-bright-one-dark soliton and one-bright-two-dark one for SW components) to the (3+1)-component YO system in detail. Then by extending the corresponding analysis to the (M+1)-component YO system, a general mixed N-soliton solution in Gram determinant form is obtained. The expression of the mixed soliton solution also contains the general all bright and all dark N-soliton solution as special cases. Besides, the dynamical analysis shows that the inelastic collision can only take place among SW components when at least two SW components have bright solitons in mixed type soliton solution. Whereas, the dark solitons in SW components and the bright soliton in LW component always undergo usual elastic collision.