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Exceptional dicretizations of the phi4 model are reviewed, correspondingconservation laws are reported, and the properties of static and movingdiscrete kinks are discussed. Different approaches to producing suchdiscretizations are given and unifying perspectives thereof are brought forth.It is also demonstrated that the high kink mobility in the exceptionaldicretizations makes it possible to analyze kink-antikink collisions in theregime of high discreteness.

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