Riemann–Hilbert approach and the soliton solutions of the discrete mKdV equations

Meisen Chen, Engui Fan and Jingsong He

Chaos, Solitons & Fractals, 2023, vol. 168, issue C

Abstract: In this paper, we present the inverse scattering transform of the discrete mKdV equation by the Riemann–Hilbert approach. By its Lax pair, we construct the Jost solution and the reflection coefficients. With these, we assume that there are higher-order zeros for the scattering coefficient a(λ), and construct the corresponding Riemann–Hilbert (RH) problem. In this vein, by the RH problem and the reconstruction formula, we obtain the multiple-pole solutions for the discrete mKdV equations. Compared with simple-pole solutions, multiple-pole solutions possess more complicated profiles.

Keywords: Discrete mKdV equation; Inverse scattering transform; Multiple-pole solution; Riemann–Hilbert problem (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923001108

DOI: 10.1016/j.chaos.2023.113209

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