Multi-dark soliton solutions of the two-dimensional multi-component Yajima-Oikawa systems

TL;DR

This paper derives and analyzes multi-dark soliton solutions for two-dimensional multi-component Yajima-Oikawa systems, revealing their elastic collision properties and bound state configurations.

Contribution

It provides the first general N-dark-dark soliton solutions for 2D and 1D multi-component Yajima-Oikawa systems using KP hierarchy reduction.

Findings

Dark-dark soliton collisions are elastic with no energy exchange.

Bound states exist up to arbitrary order for stationary cases.

Moving bound states are limited to two solitons under certain conditions.

Abstract

We present a general form of multi-dark soliton solutions of two-dimensional multi-component soliton systems. Multi-dark soliton solutions of the two-dimensional (2D) and one-dimensional (1D) multi-component Yajima-Oikawa (YO) systems, which are often called the 2D and 1D multi-component long wave-short wave resonance interaction systems, are studied in detail. Taking the 2D coupled YO system with two short wave and one long wave components as an example, we derive the general $N$-dark-dark soliton solution in both the Gram type and Wronski type determinant forms for the 2D coupled YO system via the KP hierarchy reduction method. By imposing certain constraint conditions, the general $N$-dark-dark soliton solution of the 1D coupled YO system is further obtained. The dynamics of one dark-dark and two dark-dark solitons are analyzed in detail. In contrast with bright-bright soliton collisions, it is shown that dark-dark soliton collisions are elastic and there is no energy exchange among solitons in different components. Moreover, the dark-dark soliton bound states including the stationary and moving ones are discussed. For the stationary case, the bound states exist up to arbitrary order, whereas, for the moving case, only the two-soliton bound state is possible under the condition that the coefficients of nonlinear terms have opposite signs.