Two kinds of rogue waves of the general nonlinear Schrödinger equation with derivative

Abstract

In this letter,the designable integrability(DI) of the variable coefficient derivative nonlinear Schrödinger equation (VCDNLSE) is shown by construction of an explicit transformation which maps VCDNLSE to the usual derivative nonlinear Schrödinger equation(DNLSE). One novel feature of VCDNLSE with DI is that its coefficients can be designed artificially and analytically by using transformation. What is more, from the rogue wave and rational traveling solution of the DNLSE, we get two kinds of rogue waves of the VCDNLSE by this transformation. One kind of rogue wave has vanishing boundary condition, and the other non-vanishing boundary condition. The DI of the VCDNLSE also provides a possible way to control the profile of the rogue wave in physical experiments.

arXiv comment8 pages, 5 figures

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Cited by in corpus (8)

• Breather and Rogue Wave solutions of a Generalized Nonlinear Schrodinger Equation
• Few-cycle optical rogue waves:complex modified Korteweg-de Vries equation
• Rogue Waves In Nonlinear Schrödinger Models with Variable Coefficients: Application to Bose-Einstein Condensates
• Darboux transformation of nonisospectral coupled Gross-Pitaevskii equation and its multi-component generalization
• Vector rogue waves and dark-bright boomeronic solitons in autonomous and non-autonomous settings
• Spatially modulated two- and three-component Rabi-coupled Gross-Pitaevskii systems
• Higher-order rogue wave dynamics for a derivative nonlinear Schrödinger equation
• Quasi-periodic Solutions of a Derivative Nonlinear Schrödinger Equation