About the solution of the numerical instability for topological solitons with long range interaction

TL;DR

This paper addresses numerical instabilities in simulating topological solitons with long-range interactions, proposing a constraint method that aligns numerical results closely with analytical solutions.

Contribution

It introduces a constraint technique to suppress wave-like disturbances, improving numerical stability and accuracy in soliton simulations.

Findings

The constraint improves agreement between numerical and analytical solutions.

Misalignments of SU(2) rotational axes cause instabilities.

The method effectively suppresses numerical discrepancies.

Abstract

The computations of solutions of the field equations in the Model of Topological Particles, formulated with a scalar SU(2)-field, have shown instabilities leading to discrepancies between the numerical and analytical solutions. We identify the origin of these deviations in misalignments of the rotational axes corresponding to the SU(2) elements. The system of a single soliton we use as an example to show that a constraint suppressing the wave-like disturbances is able to lead to excellent agreement between the result of the numerical minimisation procedure and the analytical solution.