A Dynamical Perspective on the ɸ4 Model Past Present and Future Panayotis G. Kevrekidis

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Product details:

• ISBN-10: 303011838X
• ISBN-13: 978-3030118389
• Author: Panayotis G. Kevrekidis, Jesús Cuevas-Maraver

This book presents a careful selection of the most important developments of the \phi^4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead.

Over the past four decades, the \phi^4 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 \phi^4 (and \phi^6, \phi^8, \phi^12 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.

Table of contents:

1. Historical Overview of the Model

2. Some Recent Developments on Kink Collisions and Related Topics

3. Collective Coordinate Methods and Their Applicability to Models

4. Mathematical Analysis of Fractal Kink-Antikink Collisions in the Model

5. Stochastic Dynamics of Kinks: Numerics and Analysis

6. Discrete Variants of the Model: Exceptional Discretizations, Conservation Laws and Related Topics

7. Discrete Breathers in and Related Models

8.  Continuum Breathers: Forty Years After

9. The Continuing Story of the Wobbling Kink

10.  Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics

11. The Model in Higher Dimensions

12. Higher-Order Field Theories: , and Beyond

13. Effects of Discrete Breathers on Thermal Transport in the Lat

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