Collective-coordinate analysis of inhomogeneous nonlinear Klein-Gordon field theory

TL;DR

This paper develops and compares two methods for deriving collective-coordinate equations to analyze solitary solutions in inhomogeneous nonlinear Klein-Gordon field theory, validated through analytical and numerical results.

Contribution

It introduces two novel approaches for deriving collective-coordinate equations for inhomogeneous NKG models and compares their effectiveness in describing soliton interactions.

Findings

Analytical expressions for soliton interactions with delta potentials.

Good agreement between analytical and numerical results.

Insights into soliton behavior in inhomogeneous media.

Abstract

Two different sets of collective-coordinate equations for solitary solutions of Nonlinear Klein-Gordon (NKG) model is introduced. The collective-coordinate equations are derived using different approaches for adding the inhomogeneities as exrernal potentials to the soliton equation of motion. Interaction of the NKG field with a local inhomogeneity like a delta function potential wall and also delta function potential well is investigated using the presented collective-coordinate equations and the results of two different models are compared. Most of the characters of the interaction are derived analytically. Analytical results are also compared with the results of numerical simulations.