Mathematical Methods in the Applied Sciences · 2010 · 109 citations · 33 references
Numerical AnalysisExp-function MethodHigher-order Nonlinear EquationsEngineeringRational Exp-function MethodNonlinear Wave PropagationSolitary TravelingNonlinear EquationNonlinear Hyperbolic ProblemIntegrable SystemPeriodic Travelling WaveModified Kudryashov MethodWave Theory
In this paper, we use the modified Kudryashov method or the rational Exp-function method to construct the solitary traveling wave solutions of the Kuramoto–Sivashinsky (shortly KS) and seventh-order Sawada–Kotera (shortly sSK) equations. These equations play a very important role in the mathematical physics and engineering sciences. Recently, Noor et al. (Noor MA, Mohyud-Din, Waheed, J. Appl. Math. Comput. 2009; 29:1–13) used the exp-function method to obtain some periodic and generalized solitary wave solutions of the KS equation. Our results improve the recent results of Noor et al. and others. Copyright © 2010 John Wiley & Sons, Ltd.
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