Hamiltonian Hopf bifurcations in the discrete nonlinear Schrodinger trimer: oscillatory instabilities, quasi-periodic solutions and a new type of self-trapping transition
2004 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, Vol. 37, no 6, 2201-2222 p.Article in journal (Refereed) Published
Oscillatory instabilities in Hamiltonian anharmonic lattices are known to appear through Hamiltonian Hopf bifurcations of certain time-periodic solutions of multibreather type. Here, we analyse the basic mechanisms for this scenario by considering the simplest possible model system of this kind where they appear: the three-site discrete nonlinear Schrodinger model with periodic boundary conditions. The stationary solution having equal amplitude and opposite phases on two sites and zero amplitude on the third is known to be unstable for an interval of intermediate amplitudes. We numerically analyse the nature of the two bifurcations leading to this instability and find them to be of two different types. Close to the lower-amplitude threshold stable two-frequency quasi-periodic solutions exist surrounding the unstable stationary solution, and the dynamics remains trapped around the latter so that in particular the amplitude of the originally unexcited site remains small. By contrast, close to the higher-amplitude threshold all two-frequency quasi-periodic solutions are detached from the unstable stationary solution, and the resulting dynamics is of population-inversion type involving also the originally unexcited site.
Place, publisher, year, edition, pages
2004. Vol. 37, no 6, 2201-2222 p.
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-53534DOI: 10.1088/0305-4470/37/6/017OAI: oai:DiVA.org:liu-53534DiVA: diva2:289476