A Dynamical Perspective on the ɸ4 Model

Past, Present and Future

  • Panayotis G. Kevrekidis
  • Jesús Cuevas-Maraver

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. David K. Campbell
    Pages 1-22
  3. Tomasz Romańczukiewicz, Yakov Shnir
    Pages 23-49
  4. Jesús Cuevas–Maraver, Panayotis G. Kevrekidis
    Pages 137-162
  5. Igor Barashenkov
    Pages 187-212
  6. Ryan M. Ross, Panayotis G. Kevrekidis, David K. Campbell, Robert Decker, Aslihan Demirkaya
    Pages 213-234
  7. Jean-Guy Caputo
    Pages 235-252
  8. Avadh Saxena, Ivan C. Christov, Avinash Khare
    Pages 253-279
  9. Back Matter
    Pages 309-311

About this book


This book presents a careful selection of the most important developments of the ɸ4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. 

Over the past four decades, the ɸ4 model has been the basis for a broad array of developments in the physics and mathematics of nonlinear waves. From kinks to breathers, from continuum media to discrete lattices, from collisions of solitary waves to spectral properties, and from deterministic to stochastic models of ɸ4 (and ɸ6812 variants more recently), this dynamical model has served as an excellent test bed for formulating and testing the ideas of nonlinear science and solitary waves.  


Kinks and Breathers Discrete and Continuum Models Solitary Wave Collisions Discrete Breathers Kink Collisions Discrete Breathers Decay of Bions Solitons

Editors and affiliations

  • Panayotis G. Kevrekidis
    • 1
  • Jesús Cuevas-Maraver
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA
  2. 2.Grupo de Física No Lineal, Universidad de SevillaDepartamento de Física Aplicada I, Escuela Politécnica SuperiorSevillaSpain

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-030-11838-9
  • Online ISBN 978-3-030-11839-6
  • Series Print ISSN 2195-9994
  • Series Online ISSN 2196-0003
  • Buy this book on publisher's site