Study of Stability of a Charged Topological Soliton in the System of Two Interacting Scalar Fields

TL;DR

This paper investigates the stability of a charged topological soliton within a system of two interacting scalar fields using analytical and numerical methods, focusing on a nonlinear spectral problem related to nonlinear field theory.

Contribution

It introduces an analytical-numerical approach to analyze a quadratic operator Hermitian pencil arising in the stability study of topological solitons in nonlinear field systems.

Findings

Characterization of the spectral problem for the soliton stability

Development of methods to analyze nonlinear spectral dependence

Insights into the stability conditions of charged topological solitons

Abstract

An analytical-numerical analysis of the singular self-adjoint spectral problem for a system of three linear ordinary second-order differential equations defined on the entire real exis is presented. This problem comes to existence in the nonlinear field theory. The dependence of the differential equations on the spectral parameter is nonlinear, which results in a quadratic operator Hermitian pencil.