On the Riemann-Hilbert problem of the Kundu equation

Beibei Hu, Ling Zhang, Tiecheng Xia and Ning Zhang

Applied Mathematics and Computation, 2020, vol. 381, issue C

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.

Keywords: Kundu equation; Initial-boundary value problem; Spectral functions; Riemann-Hilbert problem; Fokas method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320302319

DOI: 10.1016/j.amc.2020.125262

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