Four-wave mixing induced general localized waves for a coupled generalized nonlinear Schrödinger system

Abstract

In this paper, we investigate the general localized waves on the nonvanishing background for a coupled generalized nonlinear Schrödinger system with four wave mixing (FWM) effect. Using a uniform Darboux transformation, we construct a unified analytical solution formula which can be used not only to generate some reported localized waves, but also to yield some new results. Based on whether the relative wave vector of the two seed continuous-waves is zero, we respectively obtained various localized waves on the plane wave and periodic backgrounds, including bright/dark solitons, breathers, and rogue waves. Especially, we assort these localized waves and provide detailed parameter conditions for generating them, and find that the FWM term b plays a decisive role in generating the periodic background for those localized waves. In addition, interaction dynamics of the hybrid localized waves on both the plane wave and periodic backgrounds composed of the bright/dark soliton, breather and rogue wave are analyzed. We expect that these results will shed light on the understanding of localized waves on the periodic background owing to the interference of multiple continuous-wave fields.