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*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
2 Downloads (Pure)

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
Pages (from-to)2134-2170
Number of pages37
JournalCommunications in Partial Differential Equations
Volume46
Issue number11
Early online date15 Jun 2021
DOIs
Publication statusPublished - 2021

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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