Defect-mediated snaking: A new growth mechanism for localized structures

Yi-Ping Ma; J. Burke; Edgar Knobloch

doi:10.1016/j.physd.2010.06.014

Defect-mediated snaking: A new growth mechanism for localized structures

Yi-Ping Ma, J. Burke, Edgar Knobloch

Research output: Contribution to journal › Article › peer-review

70 Citations (Scopus)

Abstract

Stationary spatially localized patterns in parametrically driven systems are studied, focusing on the 2:1 and 1:1 resonance tongues as described by the forced complex Ginzburg–Landau equation. Homoclinic snaking is identified in both cases and the nature of the growth of the localized structures along the snaking branches is described. The structures grow from a central defect that inserts new rolls on either side, while pushing existing rolls outwards. This growth mechanism differs fundamentally from that found in other systems exhibiting homoclinic snaking in which new rolls are added at the fronts that connect the structure to the background homogeneous state.

Original language	English
Pages (from-to)	1867-1883
Journal	Physica D: Nonlinear Phenomena
Volume	239
Issue number	19
DOIs	https://doi.org/10.1016/j.physd.2010.06.014
Publication status	Published - 1 Oct 2010

Keywords

Localized states
Spatial dynamics
Homoclinic snaking
Forced complex Ginzburg–Landau equation

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10.1016/j.physd.2010.06.014

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title = "Defect-mediated snaking: A new growth mechanism for localized structures",

abstract = "Stationary spatially localized patterns in parametrically driven systems are studied, focusing on the 2:1 and 1:1 resonance tongues as described by the forced complex Ginzburg–Landau equation. Homoclinic snaking is identified in both cases and the nature of the growth of the localized structures along the snaking branches is described. The structures grow from a central defect that inserts new rolls on either side, while pushing existing rolls outwards. This growth mechanism differs fundamentally from that found in other systems exhibiting homoclinic snaking in which new rolls are added at the fronts that connect the structure to the background homogeneous state.",

keywords = "Localized states, Spatial dynamics, Homoclinic snaking, Forced complex Ginzburg–Landau equation",

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T1 - Defect-mediated snaking: A new growth mechanism for localized structures

AU - Ma, Yi-Ping

AU - Burke, J.

AU - Knobloch, Edgar

PY - 2010/10/1

Y1 - 2010/10/1

N2 - Stationary spatially localized patterns in parametrically driven systems are studied, focusing on the 2:1 and 1:1 resonance tongues as described by the forced complex Ginzburg–Landau equation. Homoclinic snaking is identified in both cases and the nature of the growth of the localized structures along the snaking branches is described. The structures grow from a central defect that inserts new rolls on either side, while pushing existing rolls outwards. This growth mechanism differs fundamentally from that found in other systems exhibiting homoclinic snaking in which new rolls are added at the fronts that connect the structure to the background homogeneous state.

AB - Stationary spatially localized patterns in parametrically driven systems are studied, focusing on the 2:1 and 1:1 resonance tongues as described by the forced complex Ginzburg–Landau equation. Homoclinic snaking is identified in both cases and the nature of the growth of the localized structures along the snaking branches is described. The structures grow from a central defect that inserts new rolls on either side, while pushing existing rolls outwards. This growth mechanism differs fundamentally from that found in other systems exhibiting homoclinic snaking in which new rolls are added at the fronts that connect the structure to the background homogeneous state.

KW - Localized states

KW - Spatial dynamics

KW - Homoclinic snaking

KW - Forced complex Ginzburg–Landau equation

UR - https://www.scopus.com/pages/publications/78049417343

U2 - 10.1016/j.physd.2010.06.014

DO - 10.1016/j.physd.2010.06.014

M3 - Article

SN - 0167-2789

VL - 239

SP - 1867

EP - 1883

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 19

ER -

Defect-mediated snaking: A new growth mechanism for localized structures

Abstract

Keywords

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