Generalized Fubini instantons

TL;DR

This paper constructs exact solutions for nonlinear Klein-Gordon and Euclidean $^4$ models, revealing instanton-like solutions in certain dimensions, advancing understanding of nonlinear field equations and their instanton solutions.

Contribution

It introduces a method to find exact solutions combining plane waves and rational solitons for nonlinear Klein-Gordon and $^4$ models, highlighting dimension-dependent instanton properties.

Findings

Exact solutions for nonlinear Klein-Gordon with negative coupling

Construction of instanton-like solutions in Euclidean $^4$ model

Regular instanton solutions exist only in $D\, extless=5$ dimensions

Abstract

We show that $(1+2)$ nonlinear Klein-Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows to construct the solution of similar properties for the Euclidean $\phi^4$ model with broken symmetry. Interestingly, this regular solution will be of instanton type only in the $D\le 5$ Euclidean space.