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Focusing on a line for nonlinear Schrödinger equations in \(\mathbb{R}^2\). (English) Zbl 0977.35131

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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
78A05 Geometric optics
35B40 Asymptotic behavior of solutions to PDEs
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