Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-dimensional rogue waves on zero background of the Davey-Stewartson
  II equation   A prototypical example of a rogue wave structure in a two-dimensional model
is presented in the context of the Davey-Stewartson~II (DS~II) equation arising
in water waves. The analytical methodology involves a Taylor expansion of an
eigenfunctionof the model's Lax pair which is used to form a hierarchy of
infinitely many new eigenfunctions. These are used for the construction of
two-dimensional (2D) rogue waves (RWs) of the DS~II equation by the even-fold
Darboux transformation (DT). The obtained 2D RWs, which are localized in both
space and time, can be viewed as a 2D analogue of the Peregrine soliton and are
thus natural candidates to describe oceanic RW phenomena,as well as ones in 2D
fluid systems and water tanks.

25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat