Convergence of numerical schemes for interaction equations of short and long waves. (arXiv:0912.2027v1 [math.NA])

We study numerical approximations of systems of partial differential
equations modeling the interaction of short and long waves. The short waves are
modeled by a nonlinear Schr"odinger equation which is coupled to another
equation modeling the long waves. Here, we consider the case where the long
wave equation is either a hyperbolic conservation law or a Korteweg--de Vries
equation. In the former case, we prove the strong convergence of a
Lax--Friedrichs type scheme towards the unique entropy solution of the problem,
while in the latter case we prove convergence of a finite difference scheme
towards the global solution of the problem.

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Original source : http://arxiv.org/abs/0912.2027...