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.
Wang, Solitary waves for coupled nonlinear elliptic system with nonhomogeneous nonlinearities, Calc
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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.