Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characteristic approach to the soliton resolution   As a toy model for understanding the soliton resolution phenomenon we
consider a characteristic initial boundary value problem for the 4$d$
equivariant Yang-Mills equation outside a ball. Our main objective is to
illustrate the advantages of employing outgoing null (or asymptotically null)
foliations in analyzing the relaxation processes due to the dispersal of energy
by radiation. In particular, within this approach it is evident that the
endstate of evolution must be non-radiative (meaning vanishing flux of energy
at future null infinity). In our toy model such non-radiative configurations
are given by a static solution (called the half-kink) plus an alternating chain
of $N$ decoupled kinks and antikinks. We show numerically that the
configurations $N=0$ (static half-kink) and $N=1$ (superposition of the static
half-kink and the antikink which recedes to infinity) appear as generic
attractors and we determine a codimension-one borderline between their basins
of attraction. The rates of convergence to these attractors are analyzed in
detail.

32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol