The solitary solutions of nonlinear Klein-Gordon field with minimal length

TL;DR

This paper investigates how a minimal length, predicted by quantum gravity theories, affects solitary solutions of the nonlinear Klein-Gordon field with self-interaction, deriving explicit solutions and estimating the modification parameter.

Contribution

It provides explicit solitary solutions for the modified Klein-Gordon equation incorporating minimal length effects, including energy spectrum calculations.

Findings

Explicit sech solutions for the modified field equation

Energy spectrum of solitary solutions determined

Modification parameter estimated from solution properties

Abstract

The existence of a minimal length is predicted by theories of quantum gravity and it is generally accepted that this minimal length should be of the order of the Planck length and hence can be observed in high energy phenomenon. We study the implications of the presence of the minimal length on the Klein-Gordon filed with {\phi}4self-interaction. Considering the process of spontaneous symmetry breaking, the potential also includes the {\phi}3term. The consequent field equation is a fourth-order differential equation and is considered to have solitary solutions. The sech method is applied and the normalized solutions are obtained in closed forms and the energy spectrum of the solitary fields is determined. The modification parameter of the theory is estimated by the width and the energy of the obtained solitary fields.