About long-range interaction of spheroidal solitons in scalar field nonlinear model

TL;DR

This paper investigates the long-range interactions between spheroidal solitons in a nonlinear scalar field model, revealing electromagnetic-like behavior due to nonlinearity, and provides explicit spherically symmetric solutions with Lorentz invariance.

Contribution

It introduces explicit spherically symmetric solutions for spheroidal solitons in a Born-Infeld type scalar field model and analyzes their long-range interactions, highlighting electromagnetic-like features.

Findings

Spherically symmetric soliton solutions are derived.

Long-range interactions resemble electromagnetic forces.

Interactions are caused by the model's nonlinearity.

Abstract

The nonlinear scalar field model of space-time film (Born -- Infeld type nonlinear scalar field model) is considered. Its spherically symmetrical solution is obtained. This solution gives the class of moving solitary solutions or solitons with the Lorentz transformation. We consider the distant interaction between such spheroidal solitons or spherons. This interaction is caused by the nonlinearity of the model. Starting from the static configuration with two spherons we show that the interaction under investigation is similar to electromagnetic one.