title: Recent progress on nonlinear Schrödinger systems with quadratic interactions.
abstract: The study of nonlinear Schrödinger systems with quadratic interactions has attracted much attention in the recent years. In this paper, we summarize time decay estimates of small solutions to the systems under the mass resonance condition in 2-dimensional space. We show the existence of wave operators and modified wave operators of the systems under some mass conditions in n-dimensional space, where n ≥ 2. The existence of scattering operators and finite time blow-up of the solutions for the systems in higher space dimensions is also shown.
authors.affiliation: Department of Mathematics, College of Science, Yanbian University, No.977 Gongyuan Road, Yanji, Jilin 133002, China.
authors.forename: Chunhua
authors.initials: C
authors.lastname: Li
authors.affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan.
authors.forename: Nakao
authors.initials: N
authors.lastname: Hayashi
mesh_terms: D008962:Models, Theoretical; D017711:Nonlinear Dynamics