Riemann‐Hilbert approach for multisoliton solutions of generalized coupled fourth‐order nonlinear Schrödinger equations

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 analy...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-01, Vol.43 (2), p.865-880
Main Authors: Xu, Tai‐Yang, Tian, Shou‐Fu, Peng, Wei‐Qi
Format: Article
Language:English
Subjects:
Mathematical analysis
multisoliton solutions
Nonlinear equations
Optical fibers
Optical pulses
Pulse propagation
Riemann‐Hilbert approach
Schrodinger equation
Solitary waves
Spectrum analysis
the generalized coupled fourth‐order nonlinear Schrödinger equations
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5964