Collective Coordinates in One-Dimensional Soliton Models Revisited

Abstract

We compare numerical solutions to the full field equations to simplified approaches based on implementing three collective coordinates for kink-antikink interactions within the ${\phi }^4$ and ${\varphi }^6$ models in one time and one space dimensions. We particularly pursue the question whether the collective coordinate approximation substantiates the conjecture that vibrational modes are important for resonance structures to occur in kink-antikink scattering.

12 pages, Phys. Rev. D, in print, minor changes to match proof-read version

References in corpus (2)

• Oscillons and Quasi-breathers in the ϕ^4 Klein-Gordon model
• A Mechanical Analog of the Two-bounce Resonance of Solitary Waves: Modeling and Experiment

Cited by in corpus (7)

• Spectral Walls in Soliton Collisions
• Collective coordinate model of kink-antikink collisions in ${\varphi }^4$ theory
• Kink Dynamics in a Parametric ${\varphi }^6$ System: A Model With Controllably Many Internal Modes
• Kink dynamics in a system of two coupled scalar fields in two space-time dimensions
• Topological defects with power-law tails
• Resonance structures in kink-antikink collisions in a deformed sine-Gordon model
• Singular Pöschl-Teller II potentials and gravitating kinks