Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Solutions of the Two-Dimensional Discrete Nonlinear Schr\"odinger
  Equation with Saturable Nonlinearity   We show that the two-dimensional, nonlinear Schr\"odinger lattice with a
saturable nonlinearity admits periodic and pulse-like exact solutions. We
establish the general formalism for the stability considerations of these
solutions and give examples of stability diagrams. Finally, we show that the
effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.

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The categories of this paper are: q-bio
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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: econ
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph