TL;DR
This paper studies the scattering behavior of $$ kinks in a scalar field theory, comparing numerical solutions with approximate collective coordinate models to evaluate their accuracy.
Contribution
It introduces a numerical analysis of $$ kink scattering and assesses the validity of collective coordinate approximations in modeling soliton interactions.
Findings
Numerical simulations provide detailed dynamics of $$ kink scattering.
Comparison shows the collective coordinate approximation has varying accuracy depending on conditions.
Results help improve understanding of soliton interactions in field theories.
Abstract
In this paper, we investigate the scattering of two kinks and derive the real dynamics by solving the appropriate field equation numerically employing a Runga-Kutta method. We also use a collective coordinate approximation to find approximate dynamics, with the objective being to compare the approximate motion to the real dynamics in order to test the validity of this kind of approximation, which is used extensively in the study of solitons.
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