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Research Article Open Access
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.
Lie symmetry analysis, Self-adjoint, Quasi self-adjoint, Conservation laws, Camassa-Holm equation, Degas peris-Procesi equation, Fornberg whitham equation, BBM equation, Lie Theory, Lie bracket, Lie algebra, Topology, Lie triple systems