Existence of ground states, their stability, construction of an unstable excited state, and global existence versus blow-up criteria are established for a three-wave interaction Schrödinger system in mass-critical and supercritical regimes.
Cazenave, Semilinear Schr¨ odinger Equations, Courant Lecture Notes in Mathe- matics, vol
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Standing waves for a Schr\"odinger system with three waves interaction
Existence of ground states, their stability, construction of an unstable excited state, and global existence versus blow-up criteria are established for a three-wave interaction Schrödinger system in mass-critical and supercritical regimes.