Focusing on a line for nonlinear Schrödinger equations in \(\mathbb{R}^2\) (Q2730760)
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scientific article; zbMATH DE number 1624954
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Focusing on a line for nonlinear Schrödinger equations in \(\mathbb{R}^2\) |
scientific article; zbMATH DE number 1624954 |
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29 July 2001
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nonlinear Schrödinger equations
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oscillations
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caustic
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radial focusing
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Focusing on a line for nonlinear Schrödinger equations in \(\mathbb{R}^2\) (English)
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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.
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