E. Shlizerman and V. Rom-Kedar,
Characterization of Orbits in the Truncated Nonlinear Shrödinger Model

ENOC-2005, Fifth EUROMECH Nonlinear Dynamics Conference.


The truncated and forced non-linear Schrödinger (NLS) model is analyzed using a novel framework in which a hierarchy of bifurcations is constructed. Consequently, a classification of the types of instabilities which are expected to appear due to the forcing is provided; It is shown that by introducing the forcing frequency as a free parameter (it was set to one in most of the previous studies), the behavior near the plane wave solution for any periodic box length, in the relevant amplitude regime for the truncated system, may be set to one of six different types. Furthermore, three of the six types are associated with chaotic behavior and instabilities (homoclinic chaos, hyperbolic resonance and parabolic resonance). Finally, a simple statistical measure which distinguishes between the fundamentally different types of instabilities is proposed.


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