Characteristic approach to the soliton resolution

Author(s)
Piotr Bizoń, Bradley Cownden, Maciej Maliborski
Abstract

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.

Organisation(s)
Department of Mathematics, Gravitational Physics
External organisation(s)
Jagiellonian University in Krakow
Journal
Nonlinearity
Volume
35
Pages
4585–4598
No. of pages
15
ISSN
0951-7715
DOI
https://doi.org/10.1088/1361-6544/ac7b04
Publication date
12-2021
Peer reviewed
Yes
Austrian Fields of Science 2012
103036 Theoretical physics, 101002 Analysis, 103019 Mathematical physics
Keywords
ASJC Scopus subject areas
Physics and Astronomy(all), Applied Mathematics, Statistical and Nonlinear Physics, Mathematical Physics
Portal url
https://ucris.univie.ac.at/portal/en/publications/characteristic-approach-to-the-soliton-resolution(ec8b1120-6f9e-4e63-abc7-bb7f97b724ae).html