Localized Solutions of the Non-Linear Klein-Gordon Equation in Many Dimensions

TL;DR

This paper introduces a novel complex, non-stationary, particle-like solution to the multi-dimensional non-linear Klein-Gordon equation, achieved through reduction to an ordinary differential equation.

Contribution

It provides a new method for constructing localized solutions of the non-linear Klein-Gordon equation in multiple dimensions.

Findings

Derived a new class of localized solutions

Reduced the problem to an ordinary differential equation

Demonstrated the solution's particle-like properties

Abstract

We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.