Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction
Abstract
We study the existence and stability of standing waves for a system of nonlinear Schr\"odinger equations with quadratic interaction in dimensions d≤ 3. We also study the characterization of finite time blow-up solutions with minimal mass to the system under mass resonance condition in dimension d=4. Finite time blow-up solutions with minimal mass are showed to be (up to symmetries) pseudo-conformal transformations of a ground state standing wave.
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