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A numerical study of compactons. (English) Zbl 0932.65096
Summary: The Korteweg-de Vries equation has been generalized by P. Rosenau and J. M. Hyman [Compactons: Solitons with finite wavelength, Phys. Rev. Lett. 70, No. 5, 564 (1993)] to a class of partial differential equations that has soliton solutions with compact support (compactons). Compactons are solitary waves with the remarkable soliton property that after colliding with other compactons, they re-emerge with the same coherent shape [loc. cit.]. 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 interaction of compactons have been studied. The numerical results have shown that these compactons exhibit true soliton behavior.

MSC:
65M06Finite difference methods (IVP of PDE)
35Q51Soliton-like equations
35Q53KdV-like (Korteweg-de Vries) equations
35Q55NLS-like (nonlinear Schrödinger) equations
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)