Group analysis, exact solutions and conservation laws of a generalized fifth order KdV equation

2016 ◽  
Vol 86 ◽  
pp. 8-15 ◽  
Author(s):  
Gangwei Wang ◽  
Abdul H. Kara ◽  
Kamran Fakhar ◽  
Jose Vega-Guzman ◽  
Anjan Biswas
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Group Analysis ◽  
Fifth Order

Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny–Lin equation

2017 ◽  
Vol 14 (12) ◽  
pp. 1750170 ◽  
Author(s):  
Saeede Rashidi ◽  
S. Reza Hejazi
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Group Analysis ◽  
Navier Stokes ◽  
Kawahara Equation ◽  
Navier Stokes Equation ◽  
Invariance Properties ◽  
Fractional Differential ◽  
Fifth Order ◽  
Sivashinsky Equation

This paper investigates the invariance properties of the time fractional Benny–Lin equation with Riemann–Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto–Sivashinsky equation and Navier–Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny–Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

scholarly journals Lie symmetries, conservation laws and exact solutions of a generalized quasilinear KdV equation with degenerate dispersion

2020 ◽  
Vol 13 (10) ◽  
pp. 2691-2701
Author(s):  
María-Santos Bruzón ◽  
◽  
Elena Recio ◽  
Tamara-María Garrido ◽  
Rafael de la Rosa
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Lie Symmetries

Symmetry operators and exact solutions of a type of time-fractional Burgers–KdV equation

2019 ◽  
Vol 16 (02) ◽  
pp. 1950032 ◽  
Author(s):  
Azadeh Naderifard ◽  
S. Reza Hejazi ◽  
Elham Dastranj ◽  
Ahmad Motamednezhad
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Vector Fields ◽  
Kdv Equation ◽  
Group Analysis ◽  
Invariant Subspaces ◽  
Similarity Solutions ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Symmetry Operators

In this paper, group analysis of the fourth-order time-fractional Burgers–Korteweg–de Vries (KdV) equation is considered. Geometric vector fields of Lie point symmetries of the equation are investigated and the corresponding optimal system is found. Similarity solutions of the equation are presented by using the obtained optimal system. Finally, a useful method called invariant subspaces is applied in order to find another solutions.

Sign in / Sign up

Export Citation Format

Share Document