通过Riemann-Hilbert方法求解非零边界条件下Novel Kundu-NLS方程的N孤子解
N-Soliton Solutions of Novel Kundu-NLS Equation with Non-Vanishing Asymptotic Boundary Conditions via Riemann-Hilbert Methods
DOI: 10.12677/aam.2026.154198, PDF,    科研立项经费支持
作者: 许志鹏, 张玲玲：太原理工大学数学学院，山西 太原
关键词: Riemann-Hilbert方法；Lax对；N孤子解；非零边界条件；Riemann-Hilbert Method； Lax Pair； N-Soliton； Non-Zero Boundary Condition
摘要: 本文研究了非零边界条件下Novel Kundu-NLS方程的N孤子解。首先利用变换将边界问题转化为非零常数边界问题，然后通过构造黎曼面将解析区域转换到仿射面上，对Jost解的解析性，对称性以及渐进性进行了分析，构造了广义的Riemann-Hilbert (RH)问题，通过对离散谱以及RH问题的可解性分析得到方程的N-孤子解。具体给出了孤子解在N = 1，2时候的表达式以及它们的演化图像，分析了不同参数对孤子解动力学行为的影响。
Abstract: In this paper, we focus on the N-soliton solutions of Novel Kundu-NLS equation with non-zero boundary conditions. By transforming the above equation, we have converted it into an equation with non-zero constant boundaries. Combining with the related spectral problem of the new Lax pair, the Riemann-Hilbert (RH) problem was constructed by using the Jost function and the symmetry of the scattering data. Then we obtained the N-soliton solution of the above equation through the reconstruction formula. At the end of article, we have drawn the figure of 1-soliton and 2-soliton and analyzed their dynamic behaviors.
文章引用：许志鹏, 张玲玲. 通过Riemann-Hilbert方法求解非零边界条件下Novel Kundu-NLS方程的N孤子解[J]. 应用数学进展, 2026, 15(4): 748-762. https://doi.org/10.12677/aam.2026.154198

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