Focusing of spherical nonlinear pulses in R 1+3, II. Nonlinear caustic

• Autores: Jeffrey Rauch, Rémi Carles
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 20, Nº 3, 2004, págs. 815-864
• Idioma: inglés
• DOI: 10.4171/rmi/408
• Títulos paralelos:
  • Focalización de pulsos no lineales esféricos en R1+3. II. Cáustica no lineal.
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• Resumen

  • We study spherical pulse like families of solutions to semilinear wave equattions in space time of dimension 1+3 as the pulses focus at a point and emerge outgoing. We emphasize the scales for which the incoming and outgoing waves behave linearly but the nonlinearity has a strong effect at the focus. The focus crossing is described by a scattering operator for the semilinear equation, which broadens the pulses. The relative errors in our approximate solutions are small in the L8 norm.