Parametric resonance of ground states in the nonlinear Schrödinger equation

S. Cuccagna, E. Kirr, D. Pelinovsky

Research output: Contribution to journalArticlepeer-review


We study the global existence and long-time behavior of solutions of the initial-value problem for the cubic nonlinear Schrödinger equation with an attractive localized potential and a time-dependent nonlinearity coefficient. For small initial data, we show under some nondegeneracy assumptions that the solution approaches the profile of the ground state and decays in time like t-1/4. The decay is due to resonant coupling between the ground state and the radiation field induced by the time-dependent nonlinearity coefficient.

Original languageEnglish (US)
Pages (from-to)85-120
Number of pages36
JournalJournal of Differential Equations
Issue number1
StatePublished - Jan 1 2006
Externally publishedYes


  • Asymptotic stability
  • Ground states
  • Nonlinear Schrödinger equation
  • Parametric resonance

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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