Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation

M Higuera, J Porter, E Knobloch
2002 Physica D : Non-linear phenomena  
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
more » ... ociated with cascades of gluing and symmetry-switching bifurcations; such bifurcations are located in the partial differential equations as well.
doi:10.1016/s0167-2789(01)00368-2 fatcat:bfsalwqnpjhtxojf57f4mz2qea