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A Dynamical Perspective on the ɸ4 Model

Part of the Nonlinear Systems and Complexity Book Series (volume 26)

Editors: Kevrekidis, Panayotis G.; Cuevas-Maraver, Jesús

DOI: 10.1007/978-3-030-11839-6

ISBN: 978-3-030-11838-9

Publisher: Springer International Publishing - Springer Journals

Feb 27, 2019

1 - 10 of 13 Chapters

Available

Historical Overview of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} Model

Campbell, David K.

Pages: 1 –22

[We provide an historical overview the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
Available

Some Recent Developments on Kink Collisions and Related Topics

Romańczukiewicz, Tomasz; Shnir, Yakov

Pages: 23 –49

[We review recent works on modeling of dynamics of kinks in 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
Available

Collective Coordinate Methods and Their Applicability to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} Models

Weigel, Herbert

Pages: 51 –74

[Collective coordinate methods are frequently applied to study dynamical properties of solitons. These methods simplify the field equations — typically partial differential equations — to ordinary differential equations for selected excitations. More importantly though, collective coordinates...
Available

Mathematical Analysis of Fractal Kink-Antikink Collisions in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} Model

Goodman, R. H.

Pages: 75 –91

[We analyze the fractal structure seen in kink-antikink collisions of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
Available

Stochastic Dynamics of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} Kinks: Numerics and Analysis

Lythe, Grant

Pages: 93 –110

[The stationary density of the overdamped \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
Available

Discrete Variants of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} Model: Exceptional Discretizations, Conservation Laws and Related Topics

Dmitriev, Sergey V.; Kevrekidis, Panayotis G.

Pages: 111 –136

[Exceptional dicretizations of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
Available

Discrete Breathers in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} and Related Models

Cuevas–Maraver, Jesús; Kevrekidis, Panayotis G.

Pages: 137 –162

[In this chapter, we touch upon the wide topic of discrete breathers with a special emphasis on the prototypical system of interest, namely the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
Available

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^{4}$$\end{document} Continuum Breathers: Forty Years After

Boyd, John P.

Pages: 163 –186

[More than forty years ago, a perturbation series in powers of a small parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
Available

The Continuing Story of the Wobbling Kink

Barashenkov, Igor

Pages: 187 –212

[The wobbling kink is the soliton of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
Available

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics

Ross, Ryan M.; Kevrekidis, Panayotis G.; Campbell, David K.; Decker, Robert; Demirkaya, Aslihan

Pages: 213 –234

[We explore a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi...

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