He–Laplace method for nonlinear vibration in shallow water waves

Abstract

This study is based on an analytical approach for nonlinear vibration of nonlinear evaluation equations which arises in shallow water waves. This approach is, coupled with variational iteration method and Laplace transformation, known as He–Laplace method. In order to show the capability of the proposed method, He’s polynomials are employed to handle nonlinear terms in illustrated problems due to specific limit of Laplace transformation. Significant results and their graphical representations demonstrated that He–Laplace method is most suitable for nonlinear problems, and it is enormously active for nonlinear vibrations and nonlinear waves.