Recent progress on nonlinear schrödinger systems with quadratic interactions

Chunhua Li, Nakao Hayashi

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.

Original languageEnglish
Article number214821
JournalThe Scientific World Journal
Volume2014
DOIs
Publication statusPublished - 2014
Externally publishedYes

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)

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