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Discrete Variants of the \(\phi ^4\) Model: Exceptional Discretizations, Conservation Laws and Related Topics

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A Dynamical Perspective on the ɸ4 Model

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 26))

Abstract

Exceptional dicretizations of the \(\phi ^4\) 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.

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Acknowledgements

The work of S.V.D. was supported by the grant of the Russian Science Foundation (No. 16-12-10175). This material is based upon work supported 510 by the National Science Foundation under Grant No. DMS-1809074 (P.G.K).

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Authors and Affiliations

  1. Institute for Metals Superplasticity Problems, Russian Academy of Sciences, Ufa, 450001, Russia

    Sergey V. Dmitriev

  2. National Research Tomsk State University, 36 Lenin Prospekt, 634050, Tomsk, Russia

    Sergey V. Dmitriev

  3. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA

    Panayotis G. Kevrekidis

Authors
  1. Sergey V. Dmitriev
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  2. Panayotis G. Kevrekidis
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Correspondence to Sergey V. Dmitriev .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA

    Panayotis G. Kevrekidis

  2. Grupo de Física No Lineal, Universidad de Sevilla, Departamento de Física Aplicada I, Escuela Politécnica Superior, Sevilla, Spain

    Jesús Cuevas-Maraver

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Dmitriev, S.V., Kevrekidis, P.G. (2019). Discrete Variants of the \(\phi ^4\) Model: Exceptional Discretizations, Conservation Laws and Related Topics. In: Kevrekidis, P., Cuevas-Maraver, J. (eds) A Dynamical Perspective on the ɸ4 Model. Nonlinear Systems and Complexity, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-11839-6_6

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