Constructs asymptotically self-similar global stable solutions with nonzero L² norm for some nonlinear Schrödinger equations, including two-bubble cases, and associates them with a scattering channel using the dilation operator.
A semilinear Schroedinger equation with random potential
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abstract
We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential enable us to also treat the case of small semi-linear perturbations. In both the linear and the nonlinear instances, we prove that, on average, energy remains bounded and solutions scatter.
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2022 1verdicts
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On the Existence of Self-Similar solutions for some Nonlinear Schr\"odinger equations
Constructs asymptotically self-similar global stable solutions with nonzero L² norm for some nonlinear Schrödinger equations, including two-bubble cases, and associates them with a scattering channel using the dilation operator.