Conservation laws, Lie symmetry and Painlevé analysis of the variable coefficients NNV equation

In this paper, with symbolic computation, Lie symmetry analysis, Painlevé test, conservation laws and similarity solutions for the generalized (2+1)-dimensional variable coefficients Nizhnik-Novikov-Veselov (VCNNV) equation are studied. Firstly, we derive the group classifications and the corresponding symmetry reductions via Lie group method. Then some new variable separation solutions with Lie symmetry properties are discussed. And integrable conditions of such system are determined via the Painlevé analysis. At last, some new infinite time-dependent conservation laws are derived, base on the “new conservation theorem” proved by Ibragimov.