具有高阶极点的复杂夏尔马-塔索-奥尔弗方程的黎曼-希尔伯特方法

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-06-27 DOI:10.1007/s12346-024-01053-5

Mengdie Liu, Biao Li

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引用次数: 0

摘要

通过黎曼-希尔伯特方法，考虑了具有零边界条件的复 Sharma-Tasso-Olver 方程的反散射变换。在无反射情况下，我们分别研究了一个高阶极点和多个高阶极点的黎曼-希尔伯特问题。通过黎曼-希尔伯特问题的洛朗展开和消除解中涉及的积分因子，得出了方程的显式 N 孤子解。展示了几个不同孤子的相互作用，并分析了它们的动力学。

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Riemann-Hilbert approach for the complex Sharma-Tasso-Olver equation with high-order poles

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Riemann-Hilbert approach for the complex Sharma-Tasso-Olver equation with high-order poles

The inverse scattering transform is considered for the complex Sharma-Tasso-Olver equation with zero boundary condition by Riemann-Hilbert method. Under the reflection-less situation, we investigate the Riemann-Hilbert problem with one high-order pole and multiple high-order poles, respectively. By Laurent expansion of the Riemann-Hilbert problem and elimination of the integral factor involved in the solution, the explicit N-soliton solutions of the equation are derived. The interactions of several various solitons are displayed and their dynamics are analyzed.

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.