Energy preserving integration of KdV-KdV systems - Karasozen, Bulent; Simsek, Gorkem (TWMS journal of applied and engineering mathematics, 2012)
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.