Exact Solutions of Time Dependent Korteweg-de Vries Equation by the Extended Unified Method
H. I. Abdel-Gawad1, Mohamed Osman2, Nasser S. Elazab3
1H. I. Abdel-Gawad , Mathematical Department, Cairo University, Giza, Egypt
2Mohamed Osman, Mathematical Department, Cairo University, Giza, Egypt.
3Nasser S. Elazab, Mathematical Department, Cairo University, Giza, Egypt.
Manuscript received on February 08, 2013. | Revised Manuscript received on February 29, 2013. | Manuscript published on March 05, 2013. | PP: 59-63 | Volume-3 Issue-1, March 2013. | Retrieval Number: A1298033113/2013©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Recently the unified method for finding traveling wave solutions of nonlinear evolution equations was proposed by the first author. It was shown that, this method unifies all the methods being used to find these solutions. In this paper, we extend this method to find a class of formal exact solutions to Korteweg-de Vries equation with time dependent coefficients. A new class of multiple-soliton or wave trains is obtained.
Keywords: Exact solution, Extended unified method, Korteweg-de Vries equation, Variable coefficients.