Conservation laws of KdV equation with time dependent coefficients

2011 ◽  
Vol 16 (8) ◽  
pp. 3081-3089 ◽  
Author(s):  
A.G. Johnpillai ◽  
C.M. Khalique
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Time Dependent

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.

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

Some conservation laws for a forced KdV equation

2012 ◽  
Vol 13 (6) ◽  
pp. 2692-2700 ◽  
Author(s):  
M.L. Gandarias ◽  
M.S. Bruzón
Keyword(s):  
Conservation Laws ◽  
Kdv Equation
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