Collective coordinate descriptions of a kink in a driven-damped φ⁴ model

2026/01/26 by Jacek Gatlik, Tomasz Dobrowolski, Jean-Guy Caputo +1 · 1 voice
Physics and Astronomy · #nlin.PS

paper · pdf · doi:10.1103/rf4t-lg9l

arxiv published 2026/01/26 · arxiv updated 2026/05/21

Abstract

Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of φ⁴ kinks. Three different reduced models based on the kink position, width and internal mode amplitude are introduced and compared systematically with the numerical solution of the equation with space- and time-dependent perturbations. In all cases considered, the model based on the kink position and width agrees the best with the full numerical solution. As long as the external driving frequency of the perturbation remains moderate, it captures with remarkable accuracy the intricate dynamical processes taking place in the system.

Citations

• Radial kinks in the boson stars
• Kink Dynamics in a Non-Autonomous Sine-Gordon Model
• Kink Moduli Spaces -- Collective Coordinates Reconsidered
• Collective coordinates in one-dimensional soliton models revisited
• The classical mechanics of non-conservative systems
• Front propagation into unstable states

Cited by

• Separatrix Splitting and Chaotic Dynamics in Collective-Coordinate Reductions of Driven φ⁴ Kinks

Discussions

• Jacek Gatlik, Tomasz Dobrowolski, Jean-Guy Caputo, Panayotis G. Kevrekidis: Collective coordinate descriptions of a kink in a driven-damped $\phi^4$ model https://arxiv.org/abs/2601.18940 https://arxi [bsky, 0 points, 0 comments]

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