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A PANORAMIC VIEW OF SOME PERTURBED NONLINEAR WAVE EQUATIONS

Departamento de Matemática y Física Aplicadas, Universidad Alfonso X El Sabio, Avda. Universidad 1, 28691-Villanueva de la Cañada, Madrid, Spain

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P. PASCUAL

Departamento de Ingeniería Informática, Universidad Autónoma de Madrid, Campus de Cantoblanco, Ctra. de Colmenar, km. 15, 28049 Madrid, Spain

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C. AGUIRRE

Departamento de Ingeniería Informática, Universidad Autónoma de Madrid, Campus de Cantoblanco, Ctra. de Colmenar, km. 15, 28049 Madrid, Spain

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, and

L. VÁZQUEZ

Deptartamento de Matemática Aplicada, Facultad de Informática, Universidad Complutense de Madrid, 28040 Madrid, Spain

Centro de Astrobiología, CSIC/INTA, 28850 Torrejón de Ardoz, Madrid, Spain

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https://doi.org/10.1142/S0218127404009211Cited by:21 (Source: Crossref)

Abstract

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.

Keywords:

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