Gibbs Measure for the Higher Order Modified Camassa-Holm Equation

2021 ◽  
Vol 42 (1) ◽  
pp. 105-120
Author(s):  
Lin Lin ◽  
Wei Yan ◽  
Jinqiao Duan
Keyword(s):  
Gibbs Measure ◽  
Higher Order ◽  
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.

Well-posedness and limit behaviors for a stochastic higher order modified Camassa–Holm equation

2016 ◽  
Vol 16 (06) ◽  
pp. 1650019
Author(s):  
Lin Lin ◽  
Guangying Lv ◽  
Wei Yan
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Higher Order ◽  
Well Posedness ◽  
Local Existence And Uniqueness ◽  
Holm Equation ◽  
The Cauchy Problem

This paper is devoted to the Cauchy problem for a stochastic higher order modified-Camassa–Holm equation [Formula: see text] The local existence and uniqueness with initial data [Formula: see text], [Formula: see text] and [Formula: see text], is established. The limit behaviors of the solution are examined as [Formula: see text].

scholarly journals On the Cauchy problem for a higher-order μ-Camassa-Holm equation

2018 ◽  
Vol 38 (8) ◽  
pp. 4163-4187
Author(s):  
Feng Wang ◽  
◽  
Fengquan Li ◽  
Zhijun Qiao ◽  
◽  
...  
Keyword(s):  
Cauchy Problem ◽  
Higher Order ◽  
Holm Equation ◽  
The Cauchy Problem

scholarly journals Double Reduction Analysis of Benjamin, DGH and Generalized DGH Equations

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Higher Order ◽  
Reduction Theory ◽  
Double Reduction ◽  
Linear Evolution ◽  
Holm Equation ◽  
Linear Evolution Equation ◽  
Non Linear ◽  
Benjamin Equation

The exact solutions of non-linear evolution equation, Benjamin equation, Dullin-Gottwald-Holm (DGH) equation and generalized Dullin-Gottwald-Holm equation are established using the conserved vectors. The multiplier approach is applied to construct the conserved vectors for equations under consideration. For non-linear evolution equation three conserved vectors and for Benjamin equation four conserved vectors are obtained. The conserved vectors for DGH and generalized DGH equations were reported in [1]. The higher order multiplier is considered for DGH equation and a new conserved vector is found. The double reduction theory is utilized to obtain various exact solutions for Benjamin equation, DGH equation and generalized DGH equation.

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