Title

Boundary effects on localized structures in spatially extended systems

Document Type

Article

Publication Date

7-15-2006

Abstract

We present a general method of analyzing the influence of finite size and boundary effects on the dynamics of localized solutions of non-linear spatially extended systems. The dynamics of localized structures in infinite systems involve solvability conditions that require projection onto a Goldstone mode. Our method works by extending the solvability conditions to finite sized systems, by incorporating the finite sized modifications of the Goldstone mode and associated nonzero eigenvalue. We apply this method to the special case of non-equilibrium domain walls under the influence of Dirichlet boundary conditions in a parametrically forced complex Ginzburg-Landau equation, where we examine exotic nonuniform domain wall motion due to the influence of boundary conditions. © 2006 Elsevier Ltd. All rights reserved.

Publication Source (Journal or Book title)

Physica D: Nonlinear Phenomena

First Page

142

Last Page

151

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