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arXiv · 2311.11203

The general solutions for a non-isospectral integrable TD hierarchy via the inverse scattering transform

Hongyi Zhang·Yufeng Zhang·Binlu Feng
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Abstract

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.

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Hongyi Zhang, Yufeng Zhang, Binlu Feng. 2023-11-19. The general solutions for a non-isospectral integrable TD hierarchy via the inverse scattering transform. https://arxiv.org/abs/2311.11203

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