Exact Solutions of The Shamel-Korteweg-de Vries Equation With Time Dependent Coefficients

Authors

H. I. Abdel-Gawad, Department of Mathematics, Faculty of Science, Cairo University, EgyptFollow
Mohamed Tantawy, Department of Mathematics, Faculty of Science, Cairo University, EgyptFollow

Abstract

In this paper, we present the Shamel-Korteweg-de Vries (S-KdV) equation which play an important role in studying the effect of electron trapping on the nonlinear interaction of ion-acoustic waves by including a quasi-potential. Here, a wide class of exact solutions to this equation with time dependent coefficients is found. It is shown that, the traveling wave solutions exist and they travel with time-dependent speed along the characteristic curves. The class of the obtained solutions is classified to different wave structures: periodic, elliptic or interaction of soliton, kink and anti-kink waves. The method used in this work is the extended unified method which was presented by one of the authors.

Recommended Citation

I. Abdel-Gawad, H. and Tantawy, Mohamed (2014) "Exact Solutions of The Shamel-Korteweg-de Vries Equation With Time Dependent Coefficients," Information Sciences Letters: Vol. 3 : Iss. 3 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol3/iss3/3