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- W2953261464 abstract "We study the Cauchy problem for Schrodinger equations with repulsive quadratic potential and power-like 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.
- W2953261464 created "2019-06-27" @default.
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- W2953261464 date "2002-10-31" @default.
- W2953261464 modified "2023-09-27" @default.
- W2953261464 title "Nonlinear Schrodinger equations with repulsive harmonic potential and applications" @default.
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