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Ground-state Properties of Small-Size Nonlinear Dynamical Lattices

P. Buonsante·P. Kevrekidis·V. Penna·A. Vezzani
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Abstract

We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays, and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the single-pulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the ground state (modulational) instability appears to be intimately connected with a non-standard (``double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.

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P. Buonsante, P. Kevrekidis, V. Penna, A. Vezzani. 2006-04-14. Ground-state Properties of Small-Size Nonlinear Dynamical Lattices. https://doi.org/10.1103/physreve.75.016212

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