Collective Coordinate Methods and Their Applicability to ${\phi }^4$ Models

Abstract

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 provide a practical means to focus on particular modes of otherwise complicated dynamical processes. We review the application of collective coordinate methods in the analysis of the kink-antikink interaction within the ${\phi }^4$ soliton model and illuminate discrepancies between these methods and the exact results from the field equations.

21 pages, 14 figures; invited chapter to "A dynamical perspective on the ${\phi }^4$ model: Past, present and future", Eds. P.G. Kevrekidis and J. Cuevas-Maraver; Springer book class with svmult.cls included

References in corpus (3)

• Collective Coordinates in One-Dimensional Soliton Models Revisited
• Kink Dynamics in a Parametric ${\varphi }^6$ System: A Model With Controllably Many Internal Modes
• A Mechanical Analog of the Two-bounce Resonance of Solitary Waves: Modeling and Experiment

Cited by in corpus (7)

• Solvable self-dual impurity models
• Collision of two kinks with inner structure
• Kink-antikink collisions in a weakly interacting ${\varphi }^4$ model
• Iterated ${\varphi }^4$ Kinks
• Quasinormal modes in kink excitations and kink-antikink interactions: a toy model
• Leading Quantum Correction to the ${\Phi }^4$ Kink Form Factor
• Moduli spaces for PT-regularized solitons