04-82 Eli Shlizerman and Vered Rom-Kedar

Energy surfaces and Hierarchies of bifurcations - Instabilities in the forced truncated NLS. (773K, pdf) Mar 14, 04

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Abstract. A two-degrees of freedom near integrable Hamiltonian which arises in the study of low-amplitude near-resonance envelope solutions of the forced Sine-Gordon equation is analyzed. The energy momentum bifurcation diagrams and the Fomenko graphs are constructed and reveal the bifurcation values at which the lower dimensional model exhibits instabilities and non-regular orbits of a new type. Furthermore, this study leads to some new insights regarding the \emph{hierarchy of bifurcations} appearing in integrable Hamiltonian systems and the role of global bifurcations in the energy momentum bifurcation diagrams.

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