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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 210, Number 3, Pages 331–349
DOI: https://doi.org/10.4213/tmf10055 (Mi tmf10055) 		 
This article is cited in 2 scientific papers (total 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
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DOI: https://doi.org/10.4213/tmf10055
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.
Funding agency Grant number
National Natural Science Foundation of China 11871471
11931017
Fundamental Research Funds for the Central Universities of China 00-800015Z1177
00-800015A566
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11871471 and 11931017), the Yue Qi Outstanding Scholar Project, China University of Mining & Technology, Beijing (Grant No. 00-800015Z1177), and the Fundamental Research Funds for Central Universities (Grant No. 00-800015A566).
Received: 06.01.2021
Revised: 26.07.2021
English version:
Theoretical and Mathematical Physics, 2022, Volume 210, Issue 3, Pages 287–303
DOI: https://doi.org/10.1134/S0040577922030011
Bibliographic databases:
Document Type: Article
MSC: 02.30.Ik 42.65.Tg 42.81.Dp
Language: Russian
Citation: Deqin Qiu, Cong Lv, “Riemann–Hilbert approach and $N$-soliton solutions of the generalized mixed nonlinear Schrödinger equation”, TMF, 210:3 (2022), 331–349; Theoret. and Math. Phys., 210:3 (2022), 287–303
Citation in format AMSBIB
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