Eli Shlizerman, Vered Rom-kedar
Characterization of Orbits in the Truncated and Forced Nonlinear Shr\"{o}dinger Model
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ABSTRACT.  The truncated and forced non-linear Schr\"{o}dinger (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.