Riemann-Hilbert approach for a mixed coupled nonlinear  Schrödinger equations and its soliton solutions

doi:10.52396/JUST-2021-0059

Journal of University of Science and Technology of China ›› 2021, Vol. 51 ›› Issue (3): 196-201.DOI: 10.52396/JUST-2021-0059

• Research Articles:Mathematics • Previous Articles Next Articles

Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger equations and its soliton solutions

Hu Beibei^1,2, Zhang Ling^1*, Fang Fang¹, Zhang Ning³

1. School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, China;
2. Department of Physics, Zhejiang Normal University, Jinhua 321004, China;
3. Department of Basical Courses, Shandong University of Science and Technology, Taian 271019, China

Received:2021-03-01 Revised:2021-03-20 Online:2021-03-31 Published:2021-11-16
Contact: *E-mail: originzhang@126.com

Abstract

Abstract: The integrable mixed coupled nonlinear Schrödinger (MCNLS) equations is studied, which describes the propagation of an optical pulse in a birefringent optical fiber. By the Riemann-Hilbert (RH) approach, the N-soliton solutions of the MCNLS equations can be expressed explicitly when the jump matrix of a constructed RH problem is a 3×3 unit matrix. As a special example, the expression of one soliton and two solitons are displayed explicitly. More generally, as a promotion, an integrable generalized multi-component NLS system with its linear spectral problem is discussed.

Key words: Lax pair, Riemann-Hilbert approach, mixed coupled nonlinear Schrödinger (MCNLS) equations, soliton solution, boundary conditions

CLC Number:

O175.29

HU Beibei, ZHANG Ling, FANG Fang, ZHANG Ning. Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger equations and its soliton solutions[J]. Journal of University of Science and Technology of China, 2021, 51(3): 196-201.

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Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger equations and its soliton solutions

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