Riemann-Hilbert problem of the three-component coupled Sasa-Satsuma equation and its multi-soliton solutions
Abstract
In this work, the inverse scattering transform of the three-component coupled Sasa-Satsuma equation is investigated via the Riemann-Hilbert method. Firstly we consider a Lax pair associated with a $7\times 7$ matrix spectral problem for the equation. Then we present the spectral analysis of the Lax pair, from which a kind of Riemann-Hilbert problem is formulated. Moreover, $N$-soliton solutions to the equation are constructed through a particular Riemann-Hilbert problem with vanishing scattering coefficients. Finally, the dynamics of the soliton solutions are discussed with some graphics.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.10301
- arXiv:
- arXiv:1910.10301
- Bibcode:
- 2019arXiv191010301W
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematical Physics
- E-Print:
- 17 pages, 4 figures