Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long time asymptotic for the Wadati-Konno-Ichikawa equation with finite
  density initial data   In this work, we investigate the Cauchy problem of the Wadati-Konno-Ichikawa
(WKI) equation with finite density initial data. Employing the
$\bar{\partial}$-generalization of Deift-Zhou nonlinear steepest descent
method, we derive the long time asymptotic behavior of the solution $q(x,t)$ in
space-time soliton region. Based on the resulting asymptotic behavior, the
asymptotic approximation of the WKI equation is characterized with the soliton
term confirmed by $N(I)$-soliton on discrete spectrum and the
$t^{-\frac{1}{2}}$ leading order term on continuous spectrum with residual
error up to $O(t^{-\frac{3}{4}})$. Our results also confirm the soliton
resolution conjecture for the WKI equation with finite density initial data.

16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th