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2013 Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory
Zulfiqar Ali, Syed Husnine, Imran Naeem
J. Appl. Math. 2013: 1-8 (2013). DOI: 10.1155/2013/902128

Abstract

We find exact solutions of the Generalized Modified Boussinesq (GMB) equation, the Kuromoto-Sivashinsky (KS) equation the and, Camassa-Holm (CH) equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.

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Zulfiqar Ali. Syed Husnine. Imran Naeem. "Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory." J. Appl. Math. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/902128

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950926
MathSciNet: MR3122125
Digital Object Identifier: 10.1155/2013/902128

Rights: Copyright © 2013 Hindawi

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