Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The higher-dimensional Ablowitz-Ladik model: from (non-)integrability
  and solitary waves to surprising collapse properties and more exotic
  solutions   We propose a consideration of the properties of the two-dimensional
Ablowitz-Ladik discretization of the ubiquitous nonlinear Schrodinger (NLS)
model. We use singularity confinement techniques to suggest that the relevant
discretization should not be integrable. More importantly, we identify the
prototypical solitary waves of the model and examine their stability,
illustrating the remarkable feature that near the continuum limit, this
discretization leads to the absence of collapse and complete spectral wave
stability, in stark contrast to the standard discretization of the NLS. We also
briefly touch upon the three-dimensional case and generalizations of our
considerations therein, and also present some more exotic solutions of the
model, such as exact line solitons and discrete vortices.

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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th