Heteroclinic dynamics in the parametrically driven nonlocal Schrödinger equation

Higuera Torron, Maria Jesus and Porter, Jeffrey Brent and Knobloch, Edgar (2002). Heteroclinic dynamics in the parametrically driven nonlocal Schrödinger equation. "Physica D : Nonlinear Phenomena", v. 162 (n. 3-4); pp. 155-187. ISSN 0167-2789. https://doi.org/10.1016/S0167-2789(01)00368-2.

Description

Title: Heteroclinic dynamics in the parametrically driven nonlocal Schrödinger equation
Author/s:
  • Higuera Torron, Maria Jesus
  • Porter, Jeffrey Brent
  • Knobloch, Edgar
Item Type: Article
Título de Revista/Publicación: Physica D : Nonlinear Phenomena
Date: February 2002
ISSN: 0167-2789
Volume: 162
Subjects:
Freetext Keywords: Parametric instability; Nonlinear Schrödinger equation; Global bifurcation
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Faraday waves are described, under appropriate conditions, by a damped nonlocal parametrically driven nonlinear Schrödinger equation. As the strength of the applied forcing increases this equation undergoes a sequence of transitions to chaotic dynamics. The origin of these transitions is explained using a careful study of a two-mode Galerkin truncation and linked to the presence of heteroclinic connections between the trivial state and spatially periodic standing waves. These connections are associated with cascades of gluing and symmetry-switching bifurcations; such bifurcations are located in the partial differential equations as well.

More information

Item ID: 53466
DC Identifier: http://oa.upm.es/53466/
OAI Identifier: oai:oa.upm.es:53466
DOI: 10.1016/S0167-2789(01)00368-2
Official URL: https://www.sciencedirect.com/science/article/pii/S0167278901003682
Deposited by: Memoria Investigacion
Deposited on: 13 Mar 2019 11:19
Last Modified: 13 Mar 2019 11:19
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