Some Reduction and Exact Solutions of a Higher-Dimensional Equation

Abstract

The conservation laws of the(3+1)-dimensional Zakharov-Kuznetsov equation were obtained using Noether’s theorem after an interesting substitutionu=vxto the equation. Then, with the aid of an obtained conservation law, the generalized double reduction theorem was applied to this equation. It can be verified that the reduced equation is a second order nonlinear ODE. Finally, some exact solutions of the Zakharov-Kuznetsov equation were constructed after solving the reduced equation.

Conservation Laws And The Applicability Of Group Theoretical Technique to Non-Linear Chaffee-Infante Equation

“…Employing optimal system for invariant solutions and using infinitesimal groups we would find solutions of partial differential equations, after converting them into ordinary differential equations [19], The exact analytic solutions are found by power series method. [20] 7.1.…”