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Riemann‐Hilbert approach for multisoliton solutions of generalized coupled fourth‐order nonlinear Schrödinger equations
Author(s) -
Xu TaiYang,
Tian ShouFu,
Peng WeiQi
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.5964
Subject(s) - mathematics , nonlinear system , soliton , lax pair , riemann hypothesis , riemann problem , mathematical analysis , nonlinear schrödinger equation , schrödinger equation , integrable system , physics , quantum mechanics
The main purpose of this work is to develop Riemann‐Hilbert approach to obtain the soliton solutions for generalized coupled fourth‐order nonlinear Schrödinger equations, which describe the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Starting from the spectral analysis of the Lax pair, a Riemann‐Hilbert problem is set up. After solving the obtained Riemann‐Hilbert problem with reflectionless case, we systematically derive multisoliton solutions for the generalized coupled fourth‐order nonlinear Schrödinger equations. In addition, the localized structures and dynamic behaviors of one‐ and two‐soliton solutions are shown by some graphic analysis.