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Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion
Darryl D. Holm, Ruiao Hu, Oliver D. Street, Hanchun Wang
https://arxiv.org/abs/2505.17026

Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion
We consider a coupled PDE system between the Burgers equation and the KdV equation to model the interactions between `bore'-like structures and wave-like solitons in shallow water. Two derivations of the resulting Burgers-swept KdV system are presented, based on Lie group symmetry and reduced variational principles. Exact compound soliton solutions are obtained, and numerical simulations show that the Burgers and KdV momenta tend toward a balance at which the coupled system reduces to the integ…