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

Document Type

Article

Publication Date

9-15-2008

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. © 2008 Elsevier Inc. All rights reserved.

Identifier

47949118179 (Scopus)

Publication Title

Journal of Differential Equations

External Full Text Location

https://doi.org/10.1016/j.jde.2008.06.015

e-ISSN

10902732

ISSN

00220396

First Page

1616

Last Page

1655

Issue

6

Volume

245

Grant

DMS 0510002

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