Boundary effects on localized structures in spatially extended systems

Details Boundary effects on localized structures in spatially extended systems Boundary effects on localized structures in spatially extended systems

2005-03-16

arxiv.org/abs/nlin/0503039v2

Nonlinear Sciences

Pattern Formation and Solitons

9 pages, 5 figures, submitted to Physical Review E

Scientific paper

10.1016/j.physd.2006.06.002

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.

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