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TitleA Dynamical Perspective on the ɸ4 Model [electronic resource] : Past, Present and Future / edited by Panayotis G. Kevrekidis, Jesús Cuevas-Maraver
ImprintCham : Springer International Publishing : Imprint: Springer, 2019
Edition 1st ed. 2019
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Descript XXI, 311 p. 116 illus., 84 illus. in color. online resource


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 ɸ6 ,ɸ8 ,ɸ12 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.


Historical Perspectives of \phî4 Model -- Some Recent Developments on Kink Collisions -- Statistical Mechanics and Stochastic Aspects of \phî4 Models -- Discrete Variants of \phî4 Model -- Discrete Breathers in \phî4 and Related Models -- \phî4 Breathers: History and Recent Developments -- Decay of Bions in \phî4 Models -- \phî4 Model with a Potential -- \phî4 Model in Higher Dimensions -- Beyond the \phî4 Model: \phî6, \phî8, etc.

Mathematical physics Engineering mathematics Statistical physics Mathematical Methods in Physics. Mathematical Applications in the Physical Sciences. Solid State Physics. Engineering Mathematics. Statistical Physics and Dynamical Systems.


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