Gardner, C.S., Greene, J.M., Kruskal, M.D. and Miura, R.M. (1976) Method for Solving the Korteweg-de Vries Equation. Physical Review Letters, 19, 1059-1084.

has been cited by the following article:

• TITLE: Numerical Simulation for Nonlinear Water Waves Propagating along the Free Surface

  AUTHORS: Rabab Fadhel Al-Bar

  KEYWORDS: Variational Iteration Method, Nonlinear Water Waves, Multiple Scale, Korteweg-de Vries Equations, Two Solitons Solution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.5, May 30, 2016

  ABSTRACT: The main aim of this work is to introduce the analytical approximate solutions of the water wave problem for a fluid layer of finite depth in the presence of gravity. To achieve this aim, we begun with the derivation of the Korteweg-de Vries equations for solitons by using the method of multiple scale expansion. The proposed problem describes the behavior of the system for free surface between air and water in a nonlinear approach. To solve this problem, we use the well-known analytical method, namely, variational iteration method (VIM). The proposed method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. The proposed method provides a sequence of functions which may converge to the exact solution of the proposed problem. Finally, we observe that the elevation of the water waves is in form of traveling solitary waves.