Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-time asymptotic behavior for the Novikov equation in solitonic
  regions of space time   In this paper, we study the long time asymptotic behavior for the Cauchy
problem of the Novikov equation with $3\times 3$ matrix spectral problem
\begin{align} &u_{t}-u_{txx}+4 u_{x}=3uu_xu_{xx}+u^2u_{xxx}, \nonumber &u(x,
0)=u_{0}(x),\nonumber \end{align} where $u_0(x)$ $u_0(x)\rightarrow \kappa>0, \
x\rightarrow \pm \infty$ and $u_0(x)-\kappa$ is assumed in the Schwarz space.
It is shown that the solution of the Cauchy problem can be characterized via a
Riemann-Hilbert problem in a new scale $(y,t)$ with
$$y=x-\int_{x}^{\infty}\left( (u-u_{xx}+1)^{2/3} -1\right) ds.$$ In different
space-time solitonic regions of $\xi=y/t\in (-\infty,-1/8)\cup(1,+\infty) $ and
$\xi \in(-1/8,1)$, we apply $\overline\partial$ steepest descent method to
obtain the different long time asymptotic expansions of the solution $u(y,t)$.
The corresponding residual error order is $\mathcal{O}(t^{-1+\rho})$ and
$\mathcal{O}(t^{-3/4})$ respectively from a $\overline\partial$-equation. Our
result implies that soliton resolution can be characterized with an
$N(\Lambda)$-soliton whose parameters are modulated by a sum of localized
soliton-soliton interactions as one moves through the regions.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom