This article is cited in 2 papers

Riemann–Hilbert approach and $N$-soliton solutions of the generalized mixed nonlinear Schrödinger equation

Deqin Qiu, Cong Lv

Department of Mathematics, School of Science, China University of Mining and Technology, Beijing, China

Abstract: We apply the Riemann–Hilbert method to the generalized mixed nonlinear Schrödinger equation and obtain a new formula for an explicit $N$-soliton solution, which is expressed as a ratio of $(N+1)\times(N+1)$ and $N\times N$ determinants. Using asymptotic analysis and the property of the Cauchy determinant, we derive simple elastic interactions of $N$-solitons.

Keywords: Riemann–Hilbert problem; generalized Riemann–Hilbert problem, generalized mixed nonlinear Schrödinger equation, asymptotic analysis, $N$-soliton solitonnonlinear Schrödinger equation; asymptotic analysis; $N$-soliton soliton.

MSC: 02.30.Ik 42.65.Tg 42.81.Dp

Received: 06.01.2021
Revised: 26.07.2021

DOI: 10.4213/tmf10055

 English version: Theoretical and Mathematical Physics, 2022, 210:3, 287–303

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