J L Bona et al 2008 Nonlinearity 21 2825 doi:10.1088/0951-7715/21/12/006
J L Bona1, V A Dougalis2,3 and D E Mitsotakis2,3
Show affiliationsRecommended by A L Bertozzi
In this paper we consider a coupled KdV system of Boussinesq type and its symmetric version. These systems were previously shown to possess generalized solitary waves consisting of a solitary pulse that decays symmetrically to oscillations of small, constant amplitude. We solve numerically the periodic initial-value problem for these systems using a high order accurate, fully discrete, Galerkin-finite element method. (In the case of the symmetric system, it is possible to prove rigorous, optimal-order, error estimates for this scheme.) The numerical scheme is used in an exploratory fashion to study radiating solitary-wave solutions of these systems that consist, in their simplest form, of a main, solitary-wave-like pulse that decays asymmetrically to small-amplitude, outward-propagating, oscillatory wave trains (ripples). In particular, we study the generation of radiating solitary waves, the onset of ripple formation and various aspects of the interaction and long time behaviour of these solutions.
02.70.Dh Finite-element and Galerkin methods
02.30.Jr Partial differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
37K40 Soliton theory, asymptotic behavior of solutions
35Q51 Solitons (See also 37K40)
65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Issue 12 (December 2008)
Received 10 January 2008, in final form 10 August 2008
Published 13 November 2008
J L Bona et al 2008 Nonlinearity 21 2825
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