Conservation laws of the Camassa–Holm equation

2005 ◽  
Vol 38 (4) ◽  
pp. 869-880 ◽  
Author(s):  
Jonatan Lenells
Keyword(s):  
Conservation Laws ◽  
Holm Equation

Generalized symmetries and higher-order Conservation laws of the Camassa–Holm equation

2019 ◽  
Vol 9 (2) ◽  
pp. 20-25
Author(s):  
Parastoo Kabi-Nejad ◽  
Keyword(s):  
Vector Field ◽  
Conservation Laws ◽  
Adjoint Representation ◽  
Higher Order ◽  
Optimal System ◽  
Homotopy Formula ◽  
One Dimensional ◽  
Holm Equation ◽  
Generalized Symmetries ◽  
Symmetry Criterion

In the present paper, we derive generalized symmetries of order three of the Camassa–Holm equation by infinite prolongation of a generalized vector field and applying infinitesimal symmetry criterion. In addition, one-dimensional optimal system of Lie subalgebras investigated by applying the adjoint representation. Furthermore, determining equation for multipliers and the 2- dimensional homotopy formula employed to construct higher–order conservation laws for the Camassa–Holm equation.

scholarly journals Lie symmetry and μ-symmetry methods for nonlinear generalized Camassa–Holm equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
H. Jafari ◽  
K. Goodarzi ◽  
M. Khorshidi ◽  
V. Parvaneh ◽  
Z. Hammouch
Keyword(s):  
Conservation Laws ◽  
Lie Symmetry ◽  
Lie Symmetry Method ◽  
Holm Equation ◽  
Symmetry Method

AbstractIn this paper, a Lie symmetry method is used for the nonlinear generalized Camassa–Holm equation and as a result reduction of the order and computing the conservation laws are presented. Furthermore, μ-symmetry and μ-conservation laws of the generalized Camassa–Holm equation are obtained.

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