Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ3 nonlinear response

Alex H. Ardila, Van Duong Dinh, Luigi Forcella

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We study the asymptotic dynamics for solutions to a system of nonlinear Schrödinger equations with cubic interactions, arising in nonlinear optics. We provide sharp threshold criteria leading to global well-posedness and scattering of solutions, as well as formation of singularities in finite time for (anisotropic) symmetric initial data. The free asymptotic results are proved by means of Morawetz and interaction Morawetz estimates. The blow-up results are shown by combining variational analysis and an ODE argument, which overcomes the unavailability of the convexity argument based on virial-type identities.

Original languageEnglish
JournalCommunications in Partial Differential Equations
Early online date15 Jun 2021
DOIs
Publication statusE-pub ahead of print - 15 Jun 2021

Keywords

  • Blow-up
  • cubic-type interactions
  • Morawetz estimates
  • nonlinear Schrödinger systems
  • scattering

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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