R.A. Zait, M.F. El-Sabbagh, M.F. Mourad, M.H. Abo El-Fatth
Mathematics Department
Faculty of Science
Minia University
Minia, EGYPT

Abstract. We modify both the double sine-Gordon (DSG) and triple sine-Gordon (TSG) model in (1,1) dimensions by the addition of an extra kinetic term and a potential term to their Lagrangian density and present a modified DSG (MDSG) and a modified TSG (MTSG) models. We obtain soliton solutions of the presented modified models and find that both of them possesses the same solutions of the unmodified model with some extra conditions imposed on the parameters of the models. We study some properties of the modified models, in particular, we show that the corresponding governing equation has two solutions, a special ones, which are the exact solutions of the unmodified models and a general ones, and these two types of solutions are coincides in our presented models. We end the paper with conclusions and some features and comments.

Received: April 6, 2016

AMS Subject Classification: 37K15, 35Q51, 35Q53

Key Words and Phrases: solitons, kink and double-kink solutions, double sine-gordon equation, triple sine-gordon equation

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