Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation

Abstract

Abstract:In this paper, a combined form of the Laplace transforms method with the homotopy perturbation method is proposed to solve Korteweg-DeVries (KDV) Equation. This method is called the homotopy perturbation transform method (HPTM). The (HPTM) finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results reveal that the proposed method is very efficient, simple and can be applied to other nonlinear problems.

Double Elzaki Transform Decomposition Method for Solving Third Order Korteweg-De-Vries Equations

“…So many methods and approaches have been made to find the approximate analytic solutions and numerical solutions of KdV equations, such as Adomian Decomposition Method (ADM) [1], Variation Iteration Method (VIM) [1], Homotopy Perturbation Method (HPM) [1], Homotopy Perturbation Method using Elzaki Transform [2], Homotopy Perturbation Method using Laplace Transform [3], Adomian Decomposition Method using Elzaki Transform [4], Numerical solutions to a linear KdV equation on unbounded domain [5], The numerical solutions of KdV equation using radial basis functions [6], Numerical solution of separated solitary waves for KdV equation through finite element technique [7].…”

The New Combination of Semi-Analytical Iterative Method and Elzaki Transform for Solving Some Korteweg-de Vries Equations

“…Hence, many research works have been invested in studying KDV equations, such as the Adomian decomposition method [5], the Homotopy Perturbation method [6], Temimi and Ansari method [7]. There are many attempts to combine two methods of solution, iterative methods with transformations such as the Laplace transform and the Elzaki transform, among others, Laplace Adomian decomposition method [8], [9], Homotopy Perturbation Transform Method [10], [11], Aboodh decomposition method [12], Elzaki decomposition method [13], [14].…”