Volume 10, Issue 4
Riemann-Hilbert Approach and $N$-Soliton Solutions For Three-Component Coupled Hirota Equations

East Asian J. Appl. Math., 10 (2020), pp. 717-731.

Published online: 2020-08

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• 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.

• Keywords

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

35Q51, 35Q53, 35C99, 68W30, 74J35

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@Article{EAJAM-10-717, author = {Xin Wu , and Shou-Fu Tian , and Jin-Jie Yang , }, title = {Riemann-Hilbert Approach and $N$-Soliton Solutions For Three-Component Coupled Hirota Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.170120.080420 }, url = {http://global-sci.org/intro/article_detail/eajam/17952.html} }
TY - JOUR T1 - Riemann-Hilbert Approach and $N$-Soliton Solutions For Three-Component Coupled Hirota Equations AU - Xin Wu , AU - Shou-Fu Tian , AU - Jin-Jie Yang , JO - East Asian Journal on Applied Mathematics VL - 4 SP - 717 EP - 731 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.170120.080420 UR - https://global-sci.org/intro/article_detail/eajam/17952.html KW - Three-component coupled Hirota equation, Riemann-Hilbert approach, N-soliton solution. AB -

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.

Xin Wu, Shou-Fu Tian & Jin-Jie Yang. (2020). Riemann-Hilbert Approach and $N$-Soliton Solutions For Three-Component Coupled Hirota Equations. East Asian Journal on Applied Mathematics. 10 (4). 717-731. doi:10.4208/eajam.170120.080420
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