New exact solutions for solving the initial-value-problem of the KdV–KP equation via the Lie group method

摘要

The traveling wave solutions of the two-dimensional KdV–KP equation are studied via the Lie group method. The KdV–KP equation is a nonlinear partial differential equation in two spatial and one temporal coordinate which describes the evolution of nonlinear, long waves of small amplitude with slow dependence on the transverse coordinate.The investigation of exact solutions of the KdV–KP, via the application of Lie group and the extended F-expansion methods plays the main role in understanding the nonlinear physical phenomena.