General Mixed Multi-Soliton Solutions to One-Dimensional Multicomponent Yajima-Oikawa System

TL;DR

This paper derives a comprehensive class of mixed bright-dark multi-soliton solutions for the multicomponent Yajima-Oikawa system, revealing collision behaviors and unifying various soliton configurations using the KP-hierarchy reduction method.

Contribution

It introduces a general Gram determinant form for mixed N-soliton solutions in the multicomponent Yajima-Oikawa system, encompassing all bright and dark soliton cases.

Findings

Inelastic collisions occur only among bright solitons in SW components.

Dark solitons in SW and bright solitons in LW always undergo elastic collisions.

The solutions unify all bright and dark N-soliton configurations.

Abstract

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.