标题： 非等谱可积时态发展层次的广义解通过逆散射变换 显示英文标题

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

摘要： 一种非等谱Lax对首先被引入，由此推导出一种非等谱可积TD层次，其约化是一个称为非等谱可积TD系统的可积系统。 然后通过逆散射变换(IST)方法，获得了非等谱可积TD层次的新一般孤子解。 由于我们通过IST方法研究非等谱可积系统的孤子解，需要构造一个新的Gel'fand-Levitan-Marchenko(GLM)方程。 最后，我们显式地得到了非等谱可积TD系统的精确解。 本文提出的方法可以广泛应用于其他可积方程。 显示英文摘要

摘要： 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.