On the Riemann-Hilbert problem of the Kundu equation

Abstract

The Kundu equation as a special case of the complex Ginzburg–Landau equation can be used to describe a slice of phenomena in physics and mechanics. In this paper, we analyzed the Kundu equation on the half-line by the Fokas method and proved that the potential function u(z, t) of the Kundu equation can be uniquely expressed by the solution of Riemann-Hilbert (RH) problem. It also includes the RH problem of the derivative nonlinear Schrödinger equation (also known as Kaup-Newell equation) (if ε=0), Chen–Lee–Liu equation (if ε=14) and Gerjikov–Ivanov equation (if ε=12) on the half-line.