Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rogue waves on the double periodic background in Hirota equation   We construct rogue wave solutions on the double periodic background for the
Hirota equation through one fold Darboux transformation formula. We consider
two types of double periodic solutions as seed solutions. We identify the
squared eigenfunctions and eigenvalues that appear in the one fold Darboux
transformation formula through an algebraic method with two eigenvalues. We
then construct the desired solution in two steps. In the first step, we create
double periodic waves as the background. In the second step, we build rogue
wave solution on the top of this double periodic solution. We present the
localized structures for two different values of the arbitrary parameter each
one with two different sets of eigenvalues.

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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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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: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio