Carles, Rémi Focusing on a line for nonlinear Schrödinger equations in \(\mathbb{R}^2\). (English) Zbl 0977.35131 Asymptotic Anal. 24, No. 3-4, 255-276 (2000). The author studies the asymptotics of solutions to the nonlinear Schrödinger equations, when oscillations cause concentration on a line. It is shown that when the caustic has a nonlinear influence, it can be described in terms of scattering operators. In space dimension two, when the caustic is a line, the situation is very similar to the radial focusing in one space dimension. Reviewer: Igor Andrianov (Köln) Cited in 2 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 78A05 Geometric optics 35B40 Asymptotic behavior of solutions to PDEs Keywords:nonlinear Schrödinger equations; oscillations; caustic; radial focusing PDFBibTeX XMLCite \textit{R. Carles}, Asymptotic Anal. 24, No. 3--4, 255--276 (2000; Zbl 0977.35131)