Dispersive estimates for matrix schrödinger operators in dimension two

M. Burak Erdoǧan, William R. Green

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the non-selfadjoint operator H = [ -δ + μ - V 1-V2 V2 δ - μ + V1 ] where μ < 0 and V1, V2 are real-valued decaying potentials. Such operators arise when linearizing a focusing NLS equation around a standing wave. Under natural spectral assumptions we obtain L 1(R2)×L1(R2) →; L (R2)→;L(R2) dispersive decay estimates for the evolution e<HPac. We also obtain the following weighted estimate ||w-1e ithPacf||L(R2)<L 1(R2) . 1 |t| log2(|t|) |wf|L 1(R2)×L1(R2), |t| > 2; with w(x) = log2(2 + |x|).

Original languageEnglish (US)
Pages (from-to)4473-4495
Number of pages23
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume33
Issue number10
DOIs
StatePublished - Oct 2013

Keywords

  • Asymptotic stability
  • Dispersive estimates
  • Matrix Schrödinger operators
  • Solitons
  • Weighted estimates

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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