Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping

2015 ◽  
Vol 84 (1) ◽  
pp. 135-141 ◽  
Author(s):  
R. de la Rosa ◽  
M. L. Gandarias ◽  
M. S. Bruzón
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Time Dependent ◽  
Linear Damping ◽  
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.

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

Nonlinear Self-Adjointness and Conservation Laws of KdV Equation with Linear Damping Force

2017 ◽  
Vol 5 (3) ◽  
pp. 89-94 ◽  
Author(s):  
Muhammad Nasir Ali ◽  
Shahid Ali ◽  
Syed Muhammad Husnine ◽  
Turgut Ak
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Damping Force ◽  
Linear Damping

scholarly journals Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Li-hua Zhang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Time Dependent ◽  
Group Method ◽  
New Exact Solutions ◽  
Petviashvili Equation ◽  
The Kdv Equation ◽  
Special Case

The (2 + 1)-dimensional Kadomtsev-Petviashvili equation with time-dependent coefficients is investigated. By means of the Lie group method, we first obtain several geometric symmetries for the equation in terms of coefficient functions and arbitrary functions oft. Based on the obtained symmetries, many nontrivial and time-dependent conservation laws for the equation are obtained with the help of Ibragimov’s new conservation theorem. Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. At the same time, many new exact solutions are derived such as soliton and soliton-like solutions and algebraically explicit analytical solutions.

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