Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General bright and dark soliton solutions to the massive Thirring model
  via KP hierarchy reductions   In the present paper, we are concerned with the tau function and its
connection with the Kadomtsev-Petviashvili (KP) theory for the massive Thirring
(MT) model. First, we bilinearize the massive Thirring model under both the
vanishing and nonvanishing boundary conditions. Starting from a set of bilinear
equations of two-component KP-Toda hierarchy, we derive the multi-bright
solution to the MT model by the KP hierarchy reductions. Then, we show that the
discrete KP equation can generate a set of bilinear equations of a deformed
KP-Toda hierarchy through Miwa transformation. By imposing constraints on the
parameters of the tau function, the general dark soliton solution to the MT
model is constructed from the tau function of the discrete KP equation.
Finally, the dynamics and properties of one- and two-soliton for both the
bright and dark cases are analyzed in details.

28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn