96-396 Rothos V.M., Bountis T.

MEL'NIKOV ANALYSIS OF PHASE SPACE TRANSPORT IN A N--DEGREE--OF--FREEDOM HAMILTONIAN SYSTEMS--DISCRETE NLS EQUATION (39K, LaTeX) Sep 7, 96

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Abstract. We study the connections between Mel'nikov 's analysis and phase space transport in an N--d.o.f Hamiltonian System, associated with a Discrete Nonlinear Schrodinger Equation (DNLS) with $N+1$ elements. Using the two element system as the underlying integrable subsystem we treat the coupling to the additional oscillators perturbatively. The nonintegrability of the DNLS equation with four elements has been proved by Henning et al. By means of Wiggins 's generalized Mel'nikov method, we prove nonintegrability in the arbitrary $N$ case through the existence of chaotic dynamics, study diffusion of orbits in phase space.

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