Painlevé analysis, Lie symmetries and invariant solutions of potential Kadomstev–Petviashvili equation with time dependent coefficients

摘要

In this paper, the Painlevé analysis of (2 + 1)-dimensional variable coefficients potential Kadomstev–Petviashvili (VCPKP) equation σxt+α(t)σxσxx+β(t)σxxxx+δ(t)σyy=0, has been performed to study the Painlevé properties. The VCPKP equation is also reduced to a (1 + 1)-dimensional partial differential equation via classical Lie group method and reduced equations are further studied to obtain certain general solutions.