A numerical study of adding an artificial dissipation term for solving the nonlinear dispersive equations K(n,n)K(n,n)

A linearized implicit finite difference method is devised for K(n,n)K(n,n). The stability and accuracy of the proposed methods are discussed. A compacton wave solution of the equation K(n,n)K(n,n) is used to examine the accuracy and efficiency of the proposed methods and study the effect of the added artificial dissipation term to solve the K(n,n)K(n,n) equation using finite difference method. The dynamics of waves having various initial wavepackets are discussed.