Collective Coordinate Methods and Their Applicability to $\varphi^4$ Models
Abstract
Collective coordinate methods are frequently applied to study dynamical properties of solitons. These methods simplify the field equations - typically partial differential equations - to ordinary differential equations for selected excitations. More importantly though, collective coordinates provide a practical means to focus on particular modes of otherwise complicated dynamical processes. We review the application of collective coordinate methods in the analysis of the kink-antikink interaction within the soliton model and illuminate discrepancies between these methods and the exact results from the field equations.
Keywords
Cite
@article{arxiv.1809.03772,
title = {Collective Coordinate Methods and Their Applicability to $\varphi^4$ Models},
author = {Herbert Weigel},
journal= {arXiv preprint arXiv:1809.03772},
year = {2019}
}
Comments
21 pages, 14 figures; invited chapter to "A dynamical perspective on the $\varphi^4$ model: Past, present and future", Eds. P.G. Kevrekidis and J. Cuevas-Maraver; Springer book class with svmult.cls included