Approximate method for studying the waves propagating along the interface between air-water
type: Item
instance of: scholarly article
title: Approximate method for studying the waves propagating along the interface between air-water
zbMATH Open document ID: 1213.35350
DOI: 10.1155/2011/147327
published in: Mathematical Problems in Engineering
publication date: 2011-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/229602
review text: Summary: This paper is devoted to consider the approximate solutions of the nonlinear water wave problem for a fluid layer of finite depth in the presence of gravity. The method of multiple-scale expansion is employed to obtain the Korteweg-de Vries (KdV) equations for solitons, which describes the behavior of the system for free surface between air and water in a nonlinear approach. The solutions of the water wave problem split up into two wave packets, one moving to the right and one to the left, where each of these wave packets evolves independently as the solutions of KdV equations. The solution of KdV equations is obtained analytically by using a reliable modification of Laplace decomposition method (LDM), namely, the modified Laplace decomposition method (MLDM) is presented. This procedure is a powerful tool for solving large amount of nonlinear problems. The proposed method provides the solution as a series which may converge to the exact solution of the problem. Also, the convergence analysis of the proposed method is given. Finally, we observe that the elevation of the water waves is in form of traveling solitary waves. The horizontal and vertical of the velocity components have nonlinear characters.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 5904877
Wikidata QID: Q58692364
author: M. M. Khader
author: Rabab F. Al-Bar
MaRDI profile type: Publication
OpenAlex ID: W1981833389
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description: scientific article; zbMATH DE number 5904877