Special Session 69: Lie Symmetries, Conservation laws and other approaches in solving nonlinear differential equations
Contents
In a previous work we have considered a forced Korteweg-de Vries
which serves as an analytical model of tsunami generation
by submarine landslides.
In this work we consider a damped externally excited Korteweg-de
Vries equation with a forcing term.
We derive the classical Lie symmetries admitted by the equation.
Looking for travelling waves solutions we 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 find some conservation laws for some of these
partial differential equations.