A Panoramic View of Some perturbed Nonlinear Wave Equations

In this paper we present a panoramic view of numerical simulations associated with nonlinear wave equations which appear in different experimental contexts. Mainly, we deal with scalar wave equations, but also the Maxwell equations in nonlinear media are studied. A basic part of this work is devoted to the construction and verification of numerical schemes on a physical basis. The stochastic perturbations of scalar wave equations are especially analyzed by analytical and numerical approaches. Also, other kinds of perturbations are considered, like nonlocal ones. Finally, a summary of promising experimental results from the numerical simulations of the Maxwell system in a nonlinear media is presented.

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