Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory
Joint Authors
Ali, Zulfiqar
Naeem, Imran
Husnine, Syed
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-10-31
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Ali, Zulfiqar& Husnine, Syed& Naeem, Imran. 2013. Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-506611
Modern Language Association (MLA)
Ali, Zulfiqar…[et al.]. Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory. Journal of Applied Mathematics No. 2013 (2013), pp.1-8.
https://search.emarefa.net/detail/BIM-506611
American Medical Association (AMA)
Ali, Zulfiqar& Husnine, Syed& Naeem, Imran. Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-506611
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-506611