%A Maria Jesus Higuera Torron
%A Jeffrey Brent Porter
%A Edgar Knobloch
%J Physica D : Nonlinear Phenomena
%T Heteroclinic dynamics in the parametrically driven nonlocal Schr?dinger equation
%X Faraday waves are described, under appropriate conditions, by a damped nonlocal parametrically driven nonlinear Schr?dinger 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.
%N 3-4
%K Parametric instability; Nonlinear Schr?dinger equation; Global bifurcation
%P 155-187
%V 162
%D 2002
%I Elsevier
%R 10.1016/S0167-2789(01)00368-2
%L upm53466