%0 Journal Article
%@ 0167-2789
%A Higuera Torron, Maria Jesus
%A Porter, Jeffrey Brent
%A Knobloch, Edgar
%D 2002
%F upm:53466
%I Elsevier
%J Physica D : Nonlinear Phenomena
%K Parametric instability; Nonlinear Schrödinger equation; Global bifurcation
%N 3-4
%P 155-187
%T Heteroclinic dynamics in the parametrically driven nonlocal Schrödinger equation
%U http://oa.upm.es/53466/
%V 162
%X 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.