A numerical study of K(3,2) equation

The Korteweg-de Vries (Kdv) equation has been generalized by Rosenau and Hy man [7] to a class of partial differential equations (PDEs) which has solit ary wave solution with compact support. These solitary wave solutions are c alled compactons. Compactons are solitary waves with the remarkable soliton property, that af ter colliding with other compactons, they reemerge with the same coherent s hape. These particle like waves exhibit elastic collision that are similar to the soliton interaction associated with completely integrable systems. T he point where two compactons collide are marked by a creation of low ampli tude compacton-anticompacton pair. These equations have only a finite numbe r of local conservation laws. In this paper, an implicit finite difference method and a finite element me thod have been developed to solve the K(3,2) equation. Accuracy and stabili ty of the methods have been studied. The analytical solution and the conser ved quantities are used to assess the accuracy of the suggested methods. Th e numerical results have shown that this compacton exhibits true soliton be havior.