Recent Progress on Nonlinear Schrödinger Systems with Quadratic Interactions
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 operato...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/214821 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2356-6140 1537-744X |