Iterated ϕ 4 kinks

A first order equation for a static ϕ4 kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the second iteration the kink impurity generates a kink-antikink solution or a bump solution, depending on a constant of...

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Bibliographic Details
Published in:The journal of high energy physics 2019-10, Vol.2019 (10), p.1-16
Main Authors: Manton, N S, Oleś, K, Wereszczyński, A
Format: Article
Language:English
Subjects:
Effective Field Theories
High energy physics
Impurities
Iterative methods
Linear equations
Nonperturbative Effects
Solitons Monopoles and Instantons
Online Access:Get full text
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Summary:A first order equation for a static ϕ4 kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the second iteration the kink impurity generates a kink-antikink solution or a bump solution, depending on a constant of integration. The third iterate can be a kink-antikink-kink solution or a single kink modified by a variant of the kink’s shape mode. All equations are first order ODEs, so the nth iterate has n moduli, and it is proposed that the moduli space could be used to model the dynamics of n kinks and antikinks. Curiously, fixed points of the iteration are ϕ6 kinks.
ISSN:1029-8479
DOI:10.1007/JHEP10(2019)086