General High-order Rogue Waves of the (1+1)-Dimensional Yajima–Oikawa System

Abstract

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