Focusing on a line for nonlinear Schrödinger equations in $\mathbb{R}^{2}$
Copyright policy )Focusing on a line for nonlinear Schrödinger equations in $\mathbb{R}^{2}$
This paper is devoted to the study of a semi‐classical NLS equation with a small parameter ε in two space dimensions, with oscillating data that are highly oscillating in one direction only, with the aim of modelling geometric optics with a caustic consisting of a line in $\mathbb{R}^{2}$ . We prove that the phenomena encountered are typically one‐dimensional. In order to describe the results, we introduce spaces that make it possible to define scattering operators with a parameter.
- University of Rennes 1 France
nonlinear Schrödinger equations, NLS equations (nonlinear Schrödinger equations), Asymptotic behavior of solutions to PDEs, oscillations, Geometric optics, caustic, radial focusing
nonlinear Schrödinger equations, NLS equations (nonlinear Schrödinger equations), Asymptotic behavior of solutions to PDEs, oscillations, Geometric optics, caustic, radial focusing
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