等谱和非等谱TD族,Lax表示与零曲率表示

首先，推广文「１」的结果，建立了等谱和非等谱ＴＤ族，并给出相应的Ｌａｘ表示，再用文「２」的方法得到了相应的零曲率表示。     

A non-isospectral integrable couplings of Volterra lattice hierarchy with self-consistent sources

A kind of non-isospectral integrable couplings of discrete soliton equations hierarchy with self-consistent sources associated with [Y.F. Zhang, E.G. Fan, Characteristic Numbers of Matrix Lie Algebras, Commun. Theor. Phys (China) 49 (2008) 845] is presented. As an application example, the hierarchy of non-isospectral cubic Volterra lattice hierarchy with self-consistent sources is derived. Furthermore, we construct a non-isospectral integrable couplings of cubic Volterra lattice hierarchy with self-consistent sources by using the loop algebra .     

The non-isospectral modified Kadomtsev-Petviashvili equation with self-consistent sources and its coupled system

A new algebraic method called ‘source generation procedure’ is applied to construct non-isospectral soliton equations with self-consistent sources. As results, the non-isospectral modified Kadomtsev-Petviashvili equation with self-consistent sources (mKPESCS) and its Gramm-type determinant solutions are obtained by using the source generation procedure. Furthermore, a new coupled system of the non-isospectral mKPESCS and its Pfaffian solutions are constructed.     

Grammian solutions and pfaffianization of a non-isospectral and variable-coefficient Kadomtsev-Petviashvili equation

In this paper, we first present the Grammian determinant solutions to the non-isospectral and variable-coefficient Kadomtsev-Petviashvili (vcKP) equation. Then, by using the pfaffianization procedure of Hirota and Ohta, a new non-isospectral and variable-coefficient integrable coupled system is generated. Moreover, Gramm-type pfaffian solutions of the pfaffianized system are proposed.