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We are interested in the Korteweg-de Vries (KdV), the Burgers, and theWhitham limit for a spatially periodic Boussinesq model with non-smallcontrast. We prove estimates between the KdV, the Burgers, and the Whithamapproximation and true solutions of the original system which guarantee thatthese amplitude equations make correct predictions about the dynamics of thespatially periodic Boussinesq model over the natural time scales of theamplitude equations. The proof is based on Bloch wave analysis and energyestimates. The result is the first justification result of the KdV, theBurgers, and the Whitham approximation for a dispersive PDE posed in aspatially periodic medium of non-small contrast.

The KdV, the Burgers, and the Whitham limit for a spatially periodic Boussinesq model