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- W1972522076 abstract "We study the Cauchy problem for Schrödinger equations with repulsive quadratic potential and powerlike nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the nonlinearity is focusing, we prove that choosing the harmonic potential sufficiently strong prevents blow-up in finite time. Thanks to quadratic potentials, we provide a method to anticipate, delay, or prevent wave collapse; this mechanism is explicit for critical nonlinearity." @default.
- W1972522076 created "2016-06-24" @default.
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- W1972522076 date "2003-01-01" @default.
- W1972522076 modified "2023-09-27" @default.
- W1972522076 title "Nonlinear Schrödinger Equations with Repulsive Harmonic Potential and Applications" @default.
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- W1972522076 doi "https://doi.org/10.1137/s0036141002416936" @default.
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