Approximate Solutions of Generalized Fifth-Order Korteweg-De Vries (KdV) Equation by the Standard Truncated Expansion Method

Abstract:

It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the complexity and nonlinearity, especially for non-integrable systems. In this case, some reasonable approximations of real physics are considered, by means of the standard truncated expansion approach to solve real nonlinear system is proposed. In this paper, a simple standard truncated expansion approach with a quite universal pseudopotential is used for generalized fifth-order Korteweg-de Vries (KdV) equation, we can get two kinds of approximate solutions of the above equation, in some special cases, the approximate solutions may become exact. The same idea can also used to find approximate solutions of other well known nonlinear equations. We find a quite universal expansion approach which is valid for various nonlinear partial differential equations (PDEs).

• Periodical: Applied Mechanics and Materials (Volumes 201-202)
• Pages: 246-250
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.201-202.246
• Online since: October 2012
• Authors: Jiang Long Wu, Wei Rong Yang
• Keywords: Approximate Solution, Mobious Transformation Invariance, Standard Truncated Expansion

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