A NUMERICAL STUDY OF COMPACTONS

The Korteweg-de Vries equation has been generalized by Rosenau and Hym an [Compactons: Solitons with finite wavelength, Phys. Rev. Lett. 70(5 ) (1993) 564] to a class of partial differential equations that has so liton solutions with compact support (compactons). Compactons are soli tary waves with the remarkable soliton property that after colliding w ith other compactons, they re-emerge with the same coherent shape [Ros enau and Hyman, Compactons: Solitons with finite wave length, Phys. Re v. Lett. 70(5) (1993) 564]. In this paper finite difference and finite element methods have been developed to study these types of equations . The analytical solutions and conserved quantities are used to assess the accuracy of these methods. A single compacton as well as the inte raction of compactons have been studied. The numerical results have sh own that these compactons exhibit true soliton behavior. (C) 1998 IMAC S/Elsevier Science B.V.