2005•Il Nuovo Cimento BRequires access

On soliton and other exact solutions of the combined KdV and modified and generalized KdV equations

Ashfaque Hussain Bokhari, Abdul Hamid Kara, F. D. Zaman

Abstract

In this paper we provide a rationale for using the travelling wave assumption to obtain solutions of combined KdV and modified KdV equations by using one-parameter Lie group of transformations. Some new solutions of the modified KdV equation are obtained and the procedure is applied to find the travelling wave solutions of the combined and generalized KdV equations.

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Key concepts: Korteweg–de Vries equation, Physics, Soliton, Traveling wave, Mathematical physics, Applied mathematics, Mathematical analysis, Mathematics