A generalized nonisospectral heat integrable hierarchy with three dependent variables is singled out. A Bäcklund transformation of a resulting isospectral integrable hierarchy is produced by converting the usual Lax pair into the Lax pairs in Riccati forms. In addition, an expanding integrable model is also worked out by making use of a set of linear spectral problems which are introduced via a high-dimensional loop algebra. Finally, we obtain some conserved densities of a types of heat integrable system by using the weight theory on PDEs.

中文翻译：

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广义等谱-非等谱热方程层次及其可扩展模型

提出了具有三个因变量的广义非等光谱热可积层次。通过将通常的Lax对转换为Riccati形式的Lax对，可以生成等光谱可积分层次的Bäcklund变换。此外，还利用一组通过高维循环代数引入的线性光谱问题，建立了可扩展的可积模型。最后，利用偏微分方程的权重理论，获得了一类热可积系统的守恒密度。