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.

8 pages, 5 figures

References in corpus (2)

• Harnessing and control of optical rogue waves in supercontinuum generation
• Localized nonlinear waves in systems with time- and space-modulated nonlinearities

Cited by in corpus (4)

• Few-cycle optical rogue waves:complex modified Korteweg-de Vries equation
• Vector rogue waves and dark-bright boomeronic solitons in autonomous and non-autonomous settings
• Higher-order rogue wave dynamics for a derivative nonlinear Schrödinger equation
• Quasi-periodic Solutions of a Derivative Nonlinear Schrödinger Equation