scholarly journals Approximate symmetries and conservation laws of the classical camassa–holm equation

2015 ◽  
Author(s):  
Stylianos Dimas ◽  
Igor L. Freire
Keyword(s):  
Conservation Laws ◽  
Approximate Symmetries ◽  
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.

scholarly journals Approximate symmetries and similarity solutions for wave equations on liquid films

2020 ◽  
pp. 18-18
Author(s):  
Sameerah Jamal ◽  
Andronikos Paliathanasis
Keyword(s):  
Conservation Laws ◽  
Small Amplitude ◽  
Wave Equations ◽  
Liquid Films ◽  
Similarity Solutions ◽  
Lie Symmetries ◽  
Long Waves ◽  
Approximate Symmetries ◽  
Approximate Similarity ◽  
Perturbation Parameters

We study the exact and approximate Lie symmetries for two equations which describe long waves with small amplitude on liquid films. Specifically, we study the 1+2 Benney-Luke and the 1+1 Benney-Lin equations, both from an exact and approximate perspective. To induce approximate symmetries, we show that terms involving derivatives higher than two are necessarily selected as the perturbation parameters. We construct conservation laws for both equations, and illustrate how the approximate point symmetries can be used to determine approximate similarity solutions.

Sign in / Sign up

Export Citation Format

Share Document