2023/11/19 by Hongyi Zhang, Yufeng Zhang, Zhang, Hongyi +3
Engineering · Physics and Astronomy · #Advanced Fiber Optic Sensors #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2311.11203
openalex publication_date 2023/11/19 · openalex created_date 2023/11/22 · openalex updated_date 2026/07/28
A non-isospectral Lax pair is first introduced from which a kind of non-isospectral integrable TD hierarchy is derived, whose reduction is an integrable system called the non-isospectral integrable TD system. Then by using the inverse scattering transform (IST) method, new general soliton solutions for the non-isospectral integrable TD hierarchy are obtained. Because we investigate soliton solutions of non-isospectral integrable systems by the IST method, a new Gel'fand-Levitan-Marchenko (GLM) equation needs to be constructed. Finally, we explicitly obtain the exact solutions of the non-isospectral integrable TD system. The method presented in the paper can be extensively applied to other integrable equations.