Decay of solutions of a Boussinesq-type system with variable coefficients

Abstract

We introduce a modified Chebyshev rational approximation applied to a weakly nonlinear, weakly dispersive Boussinesq formulation considered on the whole line, which is a model for waves propagating on the surface of a channel with variable bottom. We also establish rigorous convergence and error estimates in L ² of the semidiscrete and fully discrete numerical schemes and validate the numerical results using the theory derived in a previous paper on the decay of a linear pulse propagating along the surface of a channel with a random bottom.

Acknowledgements

This work was supported by the Universidad del Valle, A.A. 25360, Cali, Colombia.