ENERGY PRESERVING INTEGRATION OF KDV-KDV SYSTEMS

Year 2012, Volume: 2 Issue: 2, 219 - 227, 01.12.2012

Bulent Karasozen Gorkem Simsek

Abstract

Coupled Korteweg de Vries KdV equations in Hamiltonian form are integrated by the energy preserving average vector field AVF method. Numerical results confirm long term preservation of the energy and the quadratic invariants. Produced generalized solitary waves are similar to those in the literature for larger mesh sizes and time steps. Numerical and continuous dispersion relations of the linearized equations are compared to analyze the behavior of the traveling waves and the interaction of the solitons.

Keywords

Energy preservation, bi-Hamiltonian systems, Poisson structure, KdV equa

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