Bifurcation structure of dissipative solitons
type: Item
instance of: scholarly article
title: Bifurcation structure of dissipative solitons
zbMATH Open document ID: 1148.34033
author: N. E. Zubov
published in: Physica D
publication date: 2007-04-13T00:00:00Z
review text: Numerical bifurcation analysis of reversible system of ordinary differential equations describing stationary solutions in a model of optical cavity with external injection is performed. Two cases are considered: (i) Kerr nonlinearity when the cavity can be described by the driven-damped nonlinear Schrödinger equation (NSE) and (ii) purely dissipative nonlinearity introduced by intracavity saturable absorber. Special attention is given to fronts and localized structures corresponding to heteroclinic connections which result from intersections between the invariant manifolds of different patterned and homogeneous stationary solutions of the full PDE model. The relation between the observed phenomena and those taking place near a degenerate Hamiltonian-Hopf bifurcation is discussed.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 78A60
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 5142359
zbMATH Keywords: nonlinear optical cavities
zbMATH Keywords: pattern formation
zbMATH Keywords: reversible dynamical systems
zbMATH Keywords: homoclinic and heteroclinic bifurcations
zbMATH Keywords: localized structures
zbMATH Keywords: invariant manifolds
MaRDI profile type: Publication
full work available at URL: j.physd.2006.12.008
OpenAlex ID: W2152647360
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DOI: 10.1016/J.PHYSD.2006.12.008
description: scientific article; zbMATH DE number 5142359