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Self-similar solutions and initial values for a Schrödinger equation. (Solutions auto-similaires et espaces de données initiales pour l’équation de Schrödinger.) (French. Abridged English version) Zbl 0931.35038
Summary: We prove that for small initial data in \(\dot B_2^{1/2, \infty} (\mathbb{R}^3)\), the cubic nonlinear Schrödinger equation has solutions which are bounded in time taking values in the same Besov space, these solutions are self-similar when the initial data is homogeneous of degree \(-1\).

MSC:
35J10 Schrödinger operator, Schrödinger equation
35B99 Qualitative properties of solutions to partial differential equations
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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