EXACT SOLUTIONS FOR SOME IMPORTANT NONLINEAR PHYSICAL MODELS VIA (2+1)-DIMENSIONAL SINE-GORDON EQUATION, (2+1)-DIMENSIONAL SINH-GORDON EQUATION, DBM EQUATION AND TBD EQUATIONS

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Published: 2015-06-22

Page: 157-174


M. G. HAFEZ

Department of Mathematics, Chittagong University of Engineering and Technology, Bangladesh.

MD. NUR ALAM *

Department of Mathematics, Pabna University of Science and Technology, Bangladesh.

*Author to whom correspondence should be addressed.


Abstract

The exp(-∅(η)) -expansion method is one of the efficient methods that has appeared in recent times for establishing exact solutions to nonlinear evaluation equations (NLEEs). In this paper, the (-∅(η)) -expansion method has been applied to seek exact solutions of the (2+1)-dimensional sine-Gordon equation, (2+1)-dimensional sinh-Gordon equation, Dodd-Bullough-Mikhaiov (DBM) equation and Tzitzeica-Dodd-Bullough (TDB) equation. The results reveal that the method together with the first order ordinary differential equation is a very effective and useful tool for solving NLEEs in mathematical physics and engineering. Numerical results together with the graphical representation explicitly reveal the complete reliability and high efficiency of the proposed algorithm.

Keywords: Sine-Gordon equation, sinh-Gordon equation, DBM equation, TBD equation, traveling wave solutions, solitary wave solutions


How to Cite

HAFEZ, M. G., & ALAM, M. N. (2015). EXACT SOLUTIONS FOR SOME IMPORTANT NONLINEAR PHYSICAL MODELS VIA (2+1)-DIMENSIONAL SINE-GORDON EQUATION, (2+1)-DIMENSIONAL SINH-GORDON EQUATION, DBM EQUATION AND TBD EQUATIONS. Asian Journal of Mathematics and Computer Research, 5(3), 157–174. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/179

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