Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multilinear Operators: The Natural Extension Of Hirota's Bilinear
  Formalism   We introduce multilinear operators, that generalize Hirota's bilinear $D$
operator, based on the principle of gauge invariance of the $\tau$ functions.
We show that these operators can be constructed systematically using the
bilinear $D$'s as building blocks. We concentrate in particular on the
trilinear case and study the possible integrability of equations with one
dependent variable. The 5th order equation of the Lax-hierarchy as well as
Satsuma's lowest-order gauge invariant equation are shown to have simple
trilinear expressions. The formalism can be extended to an arbitrary degree of
multilinearity.

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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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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: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: patt-sol