Riemann--Hilbert approach and $N$-soliton solutions of the~generalized mixed nonlinear Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 331-349
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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.
@article{TMF_2022_210_3_a0,
author = {Deqin Qiu and Cong Lv},
title = {Riemann--Hilbert approach and $N$-soliton solutions of the~generalized mixed nonlinear {Schr\"odinger} equation},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {331--349},
publisher = {mathdoc},
volume = {210},
number = {3},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a0/}
}
TY - JOUR AU - Deqin Qiu AU - Cong Lv TI - Riemann--Hilbert approach and $N$-soliton solutions of the~generalized mixed nonlinear Schr\"odinger equation JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2022 SP - 331 EP - 349 VL - 210 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a0/ LA - ru ID - TMF_2022_210_3_a0 ER -
%0 Journal Article %A Deqin Qiu %A Cong Lv %T Riemann--Hilbert approach and $N$-soliton solutions of the~generalized mixed nonlinear Schr\"odinger equation %J Teoretičeskaâ i matematičeskaâ fizika %D 2022 %P 331-349 %V 210 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a0/ %G ru %F TMF_2022_210_3_a0
Deqin Qiu; Cong Lv. Riemann--Hilbert approach and $N$-soliton solutions of the~generalized mixed nonlinear Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 331-349. http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a0/