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Riemann-Hilbert Approach and $N$-Soliton Solutions for Three-Component Coupled Hirota Equations

Riemann-Hilbert Approach and $N$-Soliton Solutions for Three-Component Coupled Hirota Equations

Year:    2020

Author:    Xin Wu, Shou-Fu Tian, Jin-Jie Yang

East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 717–731

Abstract

A Riemann-Hilbert problem is employed to study integrable three-component coupled Hirota (tcCH) equations. Thus, we investigate the spectral properties of tcCH equations with a 4 × 4 Lax pair and derive a Riemann-Hilbert problem, the solution of which is used in constructing $N$-soliton solutions of the tcCH equations. While considering the spatiotemporal evolution of scattering data, the symmetry of the spectral problem is exploited. Graphical examples show new phenomena in soliton collision, including localised structures and dynamic behaviors of one- and two-soliton solutions. The results can be of interest in nonlinear dynamics of $N$-component nonlinear Schrödinger type equations.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.170120.080420

East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 717–731

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Three-component coupled Hirota equation Riemann-Hilbert approach N-soliton solution.

Author Details

Xin Wu

Shou-Fu Tian

Jin-Jie Yang