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Analytical Study on Solitary Waves and Their Interactions

Author: DuZuo
Tutor: ZongZhi
School: Dalian University of Technology
Course: Design and manufacture of ships and marine structures
Keywords: Solitary Waves Homotopy Analysis Method Homogeneous Balance Method Exact Solution Nonlinear
CLC: O353.2
Type: Master's thesis
Year: 2009
Downloads: 62
Quote: 0
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Abstract


It is an important study for obtaining the exact solution of nonlinear differential equations. The explicit solution,especially the travelling wave solution,can be used to describe the movement of surface waves well. Based the exact solution for many important equations can not still be received since the complexity of the nonlinear equations. Thus seeking new method and extending existed method,both come to an important and valuable work.In this paper,we study the initial guess in homotopy analysis mehod .Comparisons are made between the exact solution and the approximation of homotopy analysis method. Both of the analytic solutions agree well with the exact solutions. The results show that homotopy analysis method is a potential analytic method in solving nonlinear problems.Solitary wave is one of the most important types of nonlinear water waves. Quite some exact solutions of single solitary wave are available. In this paper, the interaction of two solitary waves is studied. Using the Homogeneous Balance Method (HBM), we have found the exact solutions to the nonlinear equations of water waves including Korteweg-de Vries (KdV) Equation, Boussinesq Equation, Kadomtsev-Petviashvili (KP) Equation and Nonlinear Schrodinger(NLS) Equation, which are believed to be useful for the ocean engineering.

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CLC: > Mathematical sciences and chemical > Mechanics > Fluid Mechanics > Fluid vibration and wave > Wave theory
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