Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Soliton resolution for the energy-critical nonlinear wave equation in
  the radial case   We consider the focusing energy-critical nonlinear wave equation for radially
symmetric initial data in space dimensions $D \ge 4$. This equation has a
unique (up to sign and scale) nontrivial, finite energy stationary solution
$W$, called the ground state. We prove that every finite energy solution with
bounded energy norm resolves, continuously in time, into a finite superposition
of asymptotically decoupled copies of the ground state and free radiation.

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The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th