alexa Self-adjointness, Group Classification and Conservation Laws of an Extended Camassa-Holm Equation
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

Self-adjointness, Group Classification and Conservation Laws of an Extended Camassa-Holm Equation

Nadjafikhah M1* and Pourrostami N2

1Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak-16, Tehran, Iran

2Department of Complementary Education, Payam Noor University, Tehran, Iran

Corresponding Author:
Nadjafikhah M
Department of Pure Mathematics School
of Mathematics Iran Universityof Science and
Technology, Narmak-16, Tehran, Iran
Tel:
+98 2173225426
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+982173228426
E-mail:
[email protected]

Received date: April 21, 2015; Accepted date: December 22, 2015; Published date: December 24, 2015

Citation: Nadjafikhah M, Pourrostami N (2015) Self-adjointness, Group Classification and Conservation Laws of an Extended Camassa-Holm Equation. J Generalized Lie Theory Appl S2:004. doi:10.4172/1736- 4337.S2-004

Copyright: © 2015 Nadjafikhah M, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 

Abstract

In this paper, we prove that equation 2 ( ) 2 3 = 0 t x t x x x x E ≡ u −u + u f u − au u − buu is self-adjoint and quasi self-adjoint, then we construct conservation laws for this equation using its symmetries. We investigate a symmetry classification of this nonlinear third order partial differential equation, where f is smooth function on u and a, b are arbitrary constans. We find Three special cases of this equation, using the Lie group method.

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