General high-order rogue waves of the (1+1)-dimensional Yajima-Oikawa system

TL;DR

This paper derives general high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa system using Hirota's method and KP-hierarchy reduction, revealing diverse wave patterns and the influence of an essential parameter.

Contribution

It introduces a novel derivation of high-order rogue wave solutions for the YO system, highlighting the role of an essential parameter in pattern control.

Findings

Fundamental rogue waves classified into bright, intermediate, and dark patterns.

High-order rogue waves are superpositions of fundamental waves.

An essential parameter ontrols rogue wave patterns, unlike in the nonlinear Schrdinger equation.

Abstract

General high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa (YO) system are derived by using Hirota's bilinear method and the KP-hierarchy reduction technique. These rogue wave solutions are presented in terms of determinants in which the elements are algebraic expressions. The dynamics of first and higher-order rogue wave are investigated in details for different values of the free parameters. It is shown that the fundamental (first-order) rogue waves can be classified into three different patterns: bright, intermediate and dark ones. The high-order rogue waves correspond to the superposition of fundamental rogue waves. Especially, compared with the nonlinear Schodinger equation, there exists an essential parameter \alpha to control the pattern of rogue wave for both first- and high-order rogue waves since the YO system does not possess the Galilean invariance.