Geodesic
Riemann--Hilbert problem for the~Kundu-type nonlinear Schr\"odinger equation with $N$ distinct arbitrary-order poles
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 1, pp. 23-43

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We use the Riemann–Hilbert (RH) method to study the Kundu-type nonlinear Schrödinger (Kundu–NLS) equation with a zero boundary condition in the case where the scattering coefficient has $N$ distinct arbitrary-order poles. We perform a spectral analysis of the Lax pair and consider the asymptotic property, symmetry, and analyticity of the Jost solution. Based on these results, we formulate the RH problem whose solution allows solving the considered Kundu–NLS equation. In addition, using graphic analysis, we study the characteristics of soliton solutions of some particular cases of the problem with $N$ distinct arbitrary-order poles.
Keywords: Kundu–nonlinear Schrödinger equation, zero boundary condition, Riemann–Hilbert problem, arbitrary-order pole, scattering coefficient
Mots-clés : soliton solution. 
@article{TMF_2021_207_1_a1,
     author = {Zi-Yi Wang and Shou-Fu Tian and Xiao-Fan Zhang},
     title = {Riemann--Hilbert problem for {the~Kundu-type} nonlinear {Schr\"odinger} equation with $N$ distinct arbitrary-order poles},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {23--43},
     publisher = {mathdoc},
     volume = {207},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_1_a1/}
}
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Zi-Yi Wang; Shou-Fu Tian; Xiao-Fan Zhang. Riemann--Hilbert problem for the~Kundu-type nonlinear Schr\"odinger equation with $N$ distinct arbitrary-order poles. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 1, pp. 23-43. http://geodesic.mathdoc.fr/item/TMF_2021_207_1_a1/