Abstract The extended Kadomtsev-Petviashvili (eKP) equation in fluids is investigated by using Lie symmetry analysis. reductions, together with the simplest method, are used to obtain exact solutions of eKP equation. Finally, we derive conservation laws multiplier approach.

In this paper we observe that the existence of an sl(2,R) can help us in organizing the analysis and computation of time-dependent symmetries of nonlinear evolution equations. We apply this idea to the Burgers and Ibragimov–Shabat equations. We then use sl(2,R) to compute their Bäcklund transformations. This leads to unexpected consequences for the Kadomtsev–Petviashvili equation: we show that ...

In this paper, we establish exact solutions for nonlinear evolution equations. The homogeneous balance method is used to construct exact travelling wave solutions of the CalogeroDegasperis (CD) and Potential Kadomstev-Petviashvili (PKP) equations, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many new f...