Lie Group Analysis of a Forced KdV Equation

The Korteweg-de Vries (KdV) equation considered in this work contains a forcing term and is referred to as forced KdV equation in the sequel. This equation has been investigated recently as a mathematical model for waves on shallow water surfaces under the influence of external forcing. We employ the Lie group analysis approach to specify the time-dependent forcing term

On symmetries and conservation laws of a Gardner equation involving arbitrary functions

Mathematics Subject Classification: 35C07, 35Q53In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does not require the use of a variational principle. We also construct conservation laws by using Ibragimov theorem which is based on the concept of adjoint equation for nonlinear differential equations.10 página