Convergence of numerical schemes for interaction equations of short and long waves
نویسندگان
چکیده
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 Schrödinger 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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