Abstract
In this paper, we develop a method to calculate numerical and approximate solution of some fifth-order Korteweg-de Vries equations with initial condition with the help of Laplace Decomposition Method (LDM). The technique is based on the application of Laplace transform to some fifth-order Kdv equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of four examples and results of the present technique have closed agreement with approximate solutions obtained with the help of (LDM).
Highlights
The theory of nonlinear dispersive wave motion has recently undergone much study
The Laplace decomposition method was used for finding the exact solution and approximate solution of the fifthorder Korteweg-de Vries (FKdV) (1)
The method can be easy to be extended to other nonlinear evaluation equations, with the aid of Mathematica, the course of solving nonlinear evaluation equations can be carried out in computer
Summary
The theory of nonlinear dispersive wave motion has recently undergone much study. We do not attempt to characterize the general form of nonlinear dispersive wave equations [1]. We solve a specific equation in the following nonlinear Equation (1) by using the Laplace decomposition method (LDM) [2]. Various methods for obtaining explicit solutions to nonlinear evolution equations have been proposed. We describe how the Laplace decomposition method can be used to construct the solution to the initial-value problem for the FKdV equation [1,4,5,6], ut uxxxxx F x, t, u, u2 , ux , uxx , uxxx (1). The solution of the equations, homogeneous or inhomogeneous, will be handle more quickly, and elegantly by implementing the LDM rather than the traditional methods for the approximate and numerical solutions of which are to be obtained subject to the initial condition u x, 0 g x
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