Bifurcation structure of dissipative solitons

被引：66

作者：

Gomila, Damia ^{[1
]}

Scroggie, A. J. ^{[1
]}

Firth, W. J. ^{[1
]}

机构：

[1] Univ Strathclyde, Dept Phys, Glasgow G4 0NG, Lanark, Scotland

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2007年 / 227卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

homoclinic bifurcations; localized structures; dissipative solitons; reversible systems; dynamical systems;

D O I：

10.1016/j.physd.2006.12.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we analyze in detail the structure of the phase space of a reversible dynamical system describing the stationary solutions of a model for a nonlinear optical cavity. We compare our results with the general picture described in [P.D. Woods, A.R. Champneys, Physica D 129 (1999) 147; P. Coullet, C. Riera, C. Tresser, Phys. Rev. Lett. 84 (2000) 3069] and find that the stable and unstable manifolds of homogeneous and patterned solutions present a much higher level of complexity than predicted, including the existence of additional localized solutions and fronts. This extra complexity arises due to homoclinic and heteroclinic intersections of the invariant manifolds of low-amplitude periodic solutions, and to the fact that these periodic solutions together with the high-amplitude ones constitute a one-parameter family generating a closed line on the symmetry plane. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：70 / 77

页数：8

共 23 条

[1] Cavity solitons as pixels in semiconductor microcavities [J].