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

Deqin Qiu   ; Cong Lv

Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 331-349

Résumé

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.

Détail

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.

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