Spectral analysis and soliton structures for the Hermitian symmetric space Fokas–Lenells equation
Spectral analysis and soliton structures for the Hermitian symmetric space Fokas–Lenells equation
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DOI：
10.1007/s11071-021-06892-4
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发表时间：
2021-09
影响因子：
5.6
通讯作者：
Jia Wang;X. Geng;Bo Xue
中科院分区：
文献类型：
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作者：
Jia Wang;X. Geng;Bo Xue
基于谱分析和逆散射方法，我们构造了一个与Hermitian对称空间Fokas-Lenells方程解有关的Riemann-Hilbert问题.由于该方程是一个与高阶矩阵谱问题相联系的负流，研究它是非常困难的，因此我们必须从Lax对的θ-部分而不是ex-部分开始进行谱分析，以获得足够的解析谱函数来表示所需的Riemann-Hilbert问题。相应的Riemann-Hilbert问题由Lax对的θ-部分导出，其中θ-部分只起辅助作用.揭示了Riemann-Hilbert问题的零结构，并由此在无反射情况下通过求解非正则Riemann-Hilbert问题得到了Hermitian对称空间Fokas-Lenells方程的N孤子解.此外，通过选择适当的参数，分析了多孤子解的相互作用动力学。
Based on the spectral analysis and inverse scattering method, we construct a Riemann–Hilbert problem related to the solution of the Hermitian symmetric space Fokas–Lenells equation. Because this equation is a negative flow associated with the higher-order matrix spectral problem, it is very difficult to study it. Therefore, we have to start spectral analysis from thet-part of the Lax pair other than thex-part to obtain enough analytic spectral functions formulating the desired Riemann–Hilbert problem. The corresponding Riemann–Hilbert problem is derived by thet-part of the Lax pair with thex-part playing only an auxiliary role. The zero structures of the Riemann–Hilbert problem are revealed, from whichN-soliton solutions of the Hermitian symmetric space Fokas–Lenells equation are obtained by solving the nonregular Riemann–Hilbert problem under the reflectionless case. In addition, the interaction dynamics of the multi-soliton solutions are analyzed by choosing appropriate parameters.