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The N ‐coupled higher‐order nonlinear Schrödinger equation: Riemann‐Hilbert problem and multi‐soliton solutions
Author(s) -
Yang JinJie,
Tian ShouFu,
Peng WeiQi,
Zhang TianTian
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6055
Subject(s) - breather , lax pair , mathematics , soliton , nonlinear system , riemann–hilbert problem , nonlinear schrödinger equation , mathematical physics , mathematical analysis , riemann hypothesis , schrödinger equation , physics , quantum mechanics , integrable system , boundary value problem
In this work, the Riemann‐Hilbert (RH) problem of the N ‐coupled high‐order nonlinear Schrödinger ( N ‐CHNLS) equations is studied carefully, which controls the propagation of N fields with all high‐order effects such as high‐order dispersion, self‐steepening effect, and Raman scattering in optical fiber. The spectral analysis of the Lax pair associated with a (2 N +1)×(2 N +1) matrix spectral problem for the N ‐CHNLS equations is firstly carried out, from which a kind of RH problem is structured. Then a series of multi‐soliton solutions including breather, bright, and dark solutions for the N ‐CHNLS equations can be formulated by the RH problem with the reflection‐less case. In addition, with N =4 taken as an example, the propagation behavior of these solutions and their interactions are presented by selecting appropriate parameters with some graphics.