Discrete variants of the phi4 model: exceptional discretizations, conservation laws and related topics

TL;DR

This paper reviews exceptional discretizations of the phi4 model, highlighting their conservation laws, kink properties, and high mobility, enabling advanced analysis of kink-antikink collisions in discrete systems.

Contribution

It introduces new approaches to creating exceptional discretizations and provides a unifying perspective on their properties and implications.

Findings

Exceptional discretizations exhibit high kink mobility.

Conservation laws are identified for these discretizations.

High mobility enables analysis of kink-antikink collisions in discrete regimes.

Abstract

Exceptional dicretizations of the phi4 model are reviewed, corresponding conservation laws are reported, and the properties of static and moving discrete kinks are discussed. Different approaches to producing such discretizations are given and unifying perspectives thereof are brought forth. It is also demonstrated that the high kink mobility in the exceptional dicretizations makes it possible to analyze kink-antikink collisions in the regime of high discreteness.