Solitons in systems of coupled scalar fields

TL;DR

This paper introduces a method for finding soliton solutions in relativistic coupled scalar field systems by analyzing energy bounds and deriving first-order equations, demonstrated through polynomial interaction models.

Contribution

It provides a novel approach to obtain soliton solutions in coupled scalar fields using energy considerations and first-order differential equations.

Findings

Derived first-order equations for static solutions.

Applied method to polynomial interaction systems.

Identified conditions for energy saturation.

Abstract

We present a method to obtain soliton solutions to relativistic system of coupled scalar fields. This is done by examining the energy associated to static field configurations. In this case we derive a set of first-order differential equations that solve the equations of motion when the energy saturates its lower bound. To illustrate the general results, we investigate some systems described by polynomial interactions in the coupled fields.