Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse scattering transform for the integrable nonlocal
  Lakshmanan-Porsezian-Daniel equation   In this work, a generalized nonlocal Lakshmanan-Porsezian-Daniel (LPD)
equation is introduced, and its integrability as an infinite dimensional
Hamilton dynamic system is established. Motivated by the ideas of Ablowitz and
Musslimani (2016 Nonlinearity 29 915), we successfully derive the inverse
scattering transform (IST) of the nonlocal LPD equation. The direct scattering
problem of the equation is first constructed, and some important symmetries of
the eigenfunctions and the scattering data are discussed. By using a novel
Left-Right Riemann-Hilbert (RH) problem, the inverse scattering problem is
analyzed, and the potential function is recovered. By introducing the special
conditions of reflectionless case, the time-periodic soliton solutions formula
of the equation is derived successfully. Take $J=\overline{J}=1,2,3$ and $4$
for example, we obtain some interesting phenomenon such as breather-type
solitons, arc solitons, three soliton and four soliton. Furthermore, the
influence of parameter $\delta$ on these solutions is further considered via
the graphical analysis. Finally, the eigenvalues and conserved quantities are
investigated under a few special initial conditions.

19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th