Stable solitary waves for a class of nonlinear Schrödinger system with quadratic interaction

• Main Authors: Guoqing Zhang, Tongmu Gu
• Format: Article
• Language: English
• Published: University of Szeged 2018-12-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: bound (ground) state solitary waves; quadratic interaction; variational arguments
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=6962

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 $\mathbb{R}^n$ ($n=2,3$). 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.