Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localized Nonlinear Waves on Spatio-Temporally Controllable Backgrounds
  for a (3+1)-Dimensional Kadomtsev-Petviashvili-Boussinesq Model in Water
  Waves   Physics of nonlinear waves on variable backgrounds and the relevant
mathematical analysis continues to be the challenging aspect of the study. In
this work, we consider a (3+1)-dimensional nonlinear model describing the
dynamics of {water waves} and construct nonlinear wave solutions on
spatio-temporally controllable backgrounds for the first time by using a simple
mathematical tool auto-B\"acklund transformation. Mainly, we unravel physically
interesting features to control and manipulate the dynamics of nonlinear waves
through the background. Adapting an exponential function and general polynomial
of degree two as initial seed solutions, we construct single kink-soliton and
rogue wave, respectively. We choose arbitrary periodic, localized and combined
wave backgrounds by incorporating Jacobi elliptic functions and investigate the
modulation of these two nonlinear waves with a clear analysis and graphical
demonstrations. The solutions derived in this work give us sufficient freedom
to generate exotic nonlinear coherent structures on variable backgrounds and
open up an interesting direction to explore the dynamics of various other
nonlinear waves propagating through inhomogeneous media.

15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg