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Formation of localized structures in bistable systems through nonlocal spatial coupling. II. The nonlocal Ginzburg-Landau equation. / Gelens, Lendert; Matias, M.a.; Gomila, Damia; Dorissen, Tom; Colet, P.

In: Physical Review E, Vol. 89, No. 1, 012915, 21.01.2014.

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@article{14357701cad249f0a796dcdf0be9d375,
title = "Formation of localized structures in bistable systems through nonlocal spatial coupling. II. The nonlocal Ginzburg-Landau equation",
abstract = "We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-dimensional real Ginzburg-Landau equation. While for local coupling the fronts are always monotonic and therefore the dynamical behavior leads to coarsening and the annihilation of pairs of fronts, nonlocal terms can induce spatial oscillations in the front, allowing for the creation of localized structures, emerging from pinning between two fronts.We showthis for three different nonlocal influence kernels. The first two, mod-exponential and Gaussian, are positive definite and decay exponentially or faster, while the third one, a Mexican-hat kernel, is not positive definite.",
keywords = "Physics",
author = "Lendert Gelens and M.a. Matias and Damia Gomila and Tom Dorissen and P. Colet",
year = "2014",
month = "1",
day = "21",
doi = "10.1103/PhysRevE.89.012915",
language = "English",
volume = "89",
journal = "Physical Review E. Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",
number = "1",

}

RIS

TY - JOUR

T1 - Formation of localized structures in bistable systems through nonlocal spatial coupling. II. The nonlocal Ginzburg-Landau equation

AU - Gelens, Lendert

AU - Matias, M.a.

AU - Gomila, Damia

AU - Dorissen, Tom

AU - Colet, P.

PY - 2014/1/21

Y1 - 2014/1/21

N2 - We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-dimensional real Ginzburg-Landau equation. While for local coupling the fronts are always monotonic and therefore the dynamical behavior leads to coarsening and the annihilation of pairs of fronts, nonlocal terms can induce spatial oscillations in the front, allowing for the creation of localized structures, emerging from pinning between two fronts.We showthis for three different nonlocal influence kernels. The first two, mod-exponential and Gaussian, are positive definite and decay exponentially or faster, while the third one, a Mexican-hat kernel, is not positive definite.

AB - We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-dimensional real Ginzburg-Landau equation. While for local coupling the fronts are always monotonic and therefore the dynamical behavior leads to coarsening and the annihilation of pairs of fronts, nonlocal terms can induce spatial oscillations in the front, allowing for the creation of localized structures, emerging from pinning between two fronts.We showthis for three different nonlocal influence kernels. The first two, mod-exponential and Gaussian, are positive definite and decay exponentially or faster, while the third one, a Mexican-hat kernel, is not positive definite.

KW - Physics

U2 - 10.1103/PhysRevE.89.012915

DO - 10.1103/PhysRevE.89.012915

M3 - Article

VL - 89

JO - Physical Review E. Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E. Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 1

M1 - 012915

ER -

ID: 2425311