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.
The Schroedinger Equation with Potential in Random Motion
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abstract
We study Schroedinger's equation with a potential moving along a Brownian motion path. We prove a RAGE-type theorem and Strichartz estimates for the solution on average.
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math.AP 1years
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.