A modified perturbation solution to the strongly nonlinear initial value problem of the KdV–KP equation

Abstract

In this paper, a modified perturbation method to solve strongly nonlinear initial-value-problem of the KdV–KP equation is introduced. The method is a modification of the linearized perturbation expansion method which was developed to solve nonlinear initial value problems with no small parameters. The main idea is to embed an artificial parameter so that the dependent variable can later be expanded in series of this parameter. In addition, another arbitrary constant is included to take care of the secular terms that appear after integration. The current technique assumes the arbitrary constant can also be expanded in terms of the embedded parameter. This step gives an advantage of allowing for more iteration and more correction terms to be added to the perturbation solution. The obtained solution is compared with the exact solution obtained using the Lie group method and the results show good agreement.

Keywords

• Linear perturbation method
• KdV–KP equation
• Nonlinear initial-value-problem