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Riemann–Hilbert Method for the Three-Component Sasa–Satsuma Equation and Its N-Soliton Solutions
Reports on Mathematical Physics ( IF 0.8 ) Pub Date : 2020-02-01 , DOI: 10.1016/s0034-4877(20)30012-4
Siqi Xu , Ruomeng Li , Xianguo Geng

The three-component Sasa–Satsuma equation associated with the 7 × 7 matrix spectral problem is studied by using the Riemann–Hilbert method. The spectral analysis of the Lax pair is performed for the three-component Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. As applications, N-soliton solutions for the three-component Sasa–Satsuma equation are obtained by solving the Riemann–Hilbert problems corresponding the reflectionless case. Furthermore, a compact form of N-soliton solutions formula is given explicitly, which is the ratio of (2N + 1) × (2N + 1)-determinant and (2N × 2N)-determinant.

中文翻译:

三分量Sasa-Satsuma方程的黎曼-希尔伯特方法及其N-孤子解

使用 Riemann-Hilbert 方法研究与 7 × 7 矩阵谱问题相关的三分量 Sasa-Satsuma 方程。Lax 对的谱分析是针对三分量 Sasa-Satsuma 方程进行的,从中可以制定 Riemann-Hilbert 问题。作为应用,三分量 Sasa-Satsuma 方程的 N 孤子解是通过求解对应于无反射情况的 Riemann-Hilbert 问题获得的。此外,还明确给出了N-孤子解的紧凑形式,即(2N + 1) × (2N + 1)-行列式与(2N × 2N)-行列式的比值。
更新日期:2020-02-01
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