Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A vectorial binary Darboux transformation of the first member of the
  negative part of the AKNS hierarchy   Using bidifferential calculus, we derive a vectorial binary Darboux
transformation for the first member of the "negative" part of the AKNS
hierarchy. A reduction leads to the first "negative flow" of the NLS hierarchy.
This rather simple nonlinear PDE in two dimensions with a leading mixed third
order derivative, may be regarded as describing geometric dynamics of a complex
scalar field in one dimension, since it is invariant under coordinate
transformations in one of the two independent variables. We exploit the
correspondingly reduced binary Darboux transformation to generate multi-soliton
solutions of the PDE, also with additional rational dependence on the
independent variables, and on a plane wave background. This includes rogue
waves.

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The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys