Article ID Journal Published Year Pages File Type
758036 Communications in Nonlinear Science and Numerical Simulation 2016 8 Pages PDF
Abstract

•We study a damped externally excited Korteweg-de Vries equation with a forcing term.•We derive the classical Lie symmetries admitted by the equation.•Conservation laws are established from the property of nonlinear self-adjointness.•Some exact solutions are also obtained.

In this paper we consider a damped externally excited Korteweg-de Vries (KdV) equation with a forcing term. We derive the classical Lie symmetries admitted by the equation. We then find that the damped externally excited KdV equation has some exact solutions which are periodic waves and solitary waves. These solutions are derived from the solutions of a simple nonlinear ordinary differential equation. By using a general theorem on conservation laws and the multiplier method, we construct some conservation laws for some of these partial differential equations.

Related Topics
Physical Sciences and Engineering Engineering Mechanical Engineering
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