On the Riemann-Hilbert problem of the Kundu equation

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 Schrodinger equation (also known as Kaup-Newell equation) (if epsilon = 0 ), Chen-Lee-Liu equation (if epsilon = 1/4 ) and Gerjikov-Ivanov equation (if epsilon = 1/2 ) on the half-line. (c) 2020 Elsevier Inc. All rights reserved.