RT Journal Article
SR 00
ID 10.1016/S0167-2789(01)00368-2
A1 Higuera Torron, Maria Jesus
A1 Porter, Jeffrey Brent
A1 Knobloch, Edgar
T1 Heteroclinic dynamics in the parametrically driven nonlocal Schrödinger equation
JF Physica D : Nonlinear Phenomena
YR 2002
FD 2002-02
VO 162
IS 3-4
SP 155
OP 187
K1 Parametric instability; Nonlinear Schrödinger equation; Global bifurcation
AB 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.
PB Elsevier
SN 0167-2789
LK http://oa.upm.es/53466/
UL https://www.sciencedirect.com/science/article/pii/S0167278901003682