The semistrong limit of multipulse interaction in a thermally driven optical system

Richard O. Moore, Keith Promislow

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider the semistrong limit of pulse interaction in a thermally driven, parametrically forced, nonlinear Schrödinger (TDNLS) system modeling pulse interaction in an optical cavity. The TDNLS couples a parabolic equation to a hyperbolic system, and in the semistrong scaling we construct pulse solutions which experience both short-range, tail-tail interactions and long-range thermal coupling. We extend the renormalization group (RG) methods used to derive semistrong interaction laws in reaction-diffusion systems to the hyperbolic-parabolic setting of the TDNLS system. A key step is to capture the singularly perturbed structure of the semigroup through the control of the commutator of the resolvent and a re-scaling operator. The RG approach reduces the pulse dynamics to a closed system of ordinary differential equations for the pulse locations.

Original languageEnglish (US)
Pages (from-to)1616-1655
Number of pages40
JournalJournal of Differential Equations
Volume245
Issue number6
DOIs
StatePublished - Sep 15 2008

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Nonlinear Schrödinger system
  • Renormalization group
  • Semistrong interaction

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