Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Nearest-Neighbor Interactions in Nonlinear Dynamical Lattices   We revisit the theme of non-nearest-neighbor interactions in nonlinear
dynamical lattices, in the prototypical setting of the discrete nonlinear
Schrodinger equation. Our approach offers a systematic way of analyzing the
existence and stability of solutions of the system near the so-called
anti-continuum limit of zero coupling. This affords us a number of analytical
insights such as the fact that, for instance, next-nearest-neighbor
interactions allow for solutions with nontrivial phase structure in infinite
one-dimensional lattices; in the case of purely nearest-neighbor interactions,
such phase structure is disallowed. On the other hand, such
non-nearest-neighbor interactions can critically affect the stability of
unstable structures, such as topological charge S=2 discrete vortices. These
analytical predictions are corroborated by numerical bifurcation and stability
computations.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex