Localized Properties of Rogue Wave for a Higher-Order Nonlinear Schrödinger Equation*

Abstract

Abstract In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higher-order nonlinear Schrödinger equation (HONLS) by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters α and β which denote the contribution of the higher-order terms (dispersions and nonlinear effects) included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.