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Stable solitary waves for a class of nonlinear Schrödinger system with quadratic interaction
We consider the existence and orbital stability of bound state solitary waves and ground state solitary waves for a class of nonlinear Schrödinger system with quadratic interaction in Rn (n = 2, 3). The existence of bound state and ground state solitary waves are studied by variational arguments and Concentration-compactness Lemma. In additional, we also prove the orbital stability of bound state and ground state solitary waves