ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Soliton Solutions of the Long-Short Wave Equation with Power Law Nonlinearity

Journal of Applied Nonlinear Dynamics 1(2) (2012) 125--140 | DOI:10.5890/JAND.2012.05.002

Manel Labidi $^{1}$, Houria Triki $^{2}$, E.V. Krishnan $^{3}$, Anjan Biswas $^{4}$

$^{1}$ Laboratory of Engineering Mathematics, Tunisia Polytechnic School, University of 7th November at Carthage, BP 743, La Marsa 2070, TUNISIA

$^{2}$ Radiation Physics Laboratory, Department of Physics, Badji Mokhtar University, 2300 Anaba, ALGERIA

$^{3}$ Department of Mathematics and Statistics, Sultan Qaboos University, P. O. Box 36, Al Khod 123, Muscat, OMAN

$^{4}$ Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA

Abstract

This paper studies the generalized long-short wave equation with power law nonlinearity. There are several approaches that are used to solve this coupled system nonlinear evolution equations. The series solution approach yields the topological 1-soliton solution or shock wave solution. The ansatz method and the semiinverse variational principle leads to the non-topological 1-soliton of the equation. Additionally, the variational iteration method is used to study the equation. Finally, numerical simulations are also given to this equation.

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