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Waves in Random and Complex Media Volume 21, 2011 - Issue 4
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Original Articles

Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

Ghodrat Ebadi Faculty of Mathematical Sciences, University of Tabriz, Tabriz 51666-14766, Iran
,
E.V. Krishnan Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Muscat, Al Khod 123, Sultanate of Oman
,
Manel Labidi Laboratory of Engineering Mathematics, Tunisia Polytechnic School, University of 7th November at Carthage, BP 743, La Marsa 2070, Tunisia
,
Essaid Zerrad Department of Physics and Pre-Engineering, Delaware State University, Dover, DE 19901-2277, USA
&
Anjan Biswas Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USACorrespondence[email protected]
Pages 559-590 | Received 10 Jan 2011, Accepted 07 Jul 2011, Published online: 18 Aug 2011
 
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Abstract

This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis.

Acknowledgements

The research work of the last two authors (EZ and AB) was fully supported by the Army Research Office (ARO) and the Air Force Office of Scientific Research (AFOSR) under the award number: W54428-RT-ISP and this support is gratefully recognized.

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