## Journal of Generalized Lie Theory and Applications

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

#### Abstract

In this paper, we prove that equation $E ≡ u_1-u_{_x2_t}+u_xf(u)-au_xu_{}x^2-buu_{x^3}=0$ 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.

#### Article information

Source
J. Gen. Lie Theory Appl., Volume 10, Number S2 (2016), 5 pages.

Dates
First available in Project Euclid: 16 November 2016

https://projecteuclid.org/euclid.jglta/1479265223

Digital Object Identifier
doi:10.4172/1736-4337.1000S2-004

Mathematical Reviews number (MathSciNet)
MR3663973

Zentralblatt MATH identifier
1371.35253

#### Citation

Nadjafikhah, M; Pourrostami, N. Self-adjointness, Group Classification and Conservation Laws of an Extended Camassa-Holm Equation. J. Gen. Lie Theory Appl. 10 (2016), no. S2, 5 pages. doi:10.4172/1736-4337.1000S2-004. https://projecteuclid.org/euclid.jglta/1479265223