Carles, Rémi; Rauch, Jeffrey Focusing of spherical nonlinear pulses in \(\mathbb{R}^{1+3}\) and scattering. (Diffusion d’impulsions non linéaires radiales focalisantes dans \(\mathbb{R}^{1+3}\).) (French. Abridged English version) Zbl 0985.35045 C. R. Acad. Sci., Paris, Sér. I, Math. 332, No. 12, 1077-1082 (2001). Summary: We study the validity of geometric optics for nonlinear wave equations in three space dimensions whose solutions, pulse like, focus at a point. If the amplitude of the initial data is critical, linear geometric optics is valid before the focal point, as well as after. The matching between these two regimes is described by a scattering operator, which enlarges the support of the waves. Cited in 2 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 78A05 Geometric optics Keywords:critical initial data; nonlinear wave equations in three space dimensions PDFBibTeX XMLCite \textit{R. Carles} and \textit{J. Rauch}, C. R. Acad. Sci., Paris, Sér. I, Math. 332, No. 12, 1077--1082 (2001; Zbl 0985.35045) Full Text: DOI