Binary Bell polynomial approach to the non-isospectral and variable-coefficient KP equations

In this paper, binary Bell polynomial approach is extended to systematically investigate bilinear representations, bilinear Bäcklund transformations and Lax pairs for a generalized non-isospectral Kadomtsev-Petviashvili (KP) (NKP) equation and a generalized variable-coefficient KP (GKP) equation studied by Clarkson. The integrable constraint conditions on the variable coefficients can be naturally found in the procedure of applying the Bell polynomials. It is very interesting that, for the GKP equation, the eigenvalues in Lax pair may be y- and t-dependent functions, which exactly satisfy Riemann wave equations like breaking soliton equation. The results presented in this paper may provide further evidence of structures and complete integrability of these equations. © The Author 2011. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.