Exact Solutions of Generalized Modified Boussinesq, Kuramoto‐Sivashinsky, and Camassa‐Holm Equations via Double Reduction Theory

Zulfiqar Ali, Syed Husnine and Imran Naeem

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/902128

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:902128

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().