Focusing of spherical nonlinear pulses in \(\mathbb R^{1+3}\). II: Nonlinear caustic
Summary: For parts I and III see [Proc. Am. Math. Soc. 130, No. 3, 791--804 (2002; Zbl 0953.35089) and Tôhoku Math. J. (2) 56, No. 3, 393--410 (2004; Zbl 1095.35010)]. We study spherical pulse like families of solutions to semilinear wave equations 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 \(L^\infty\) norm.
scientific article; zbMATH DE number 2156859