Dispersion relation of the non-linear Klein-Gordon equation through a variational method

TL;DR

This paper develops a fully analytical variational method based on the Linear Delta Expansion to derive approximate dispersion relations for the nonlinear Klein-Gordon equation, improving accuracy and simplicity over existing methods.

Contribution

It introduces a new variational approach that provides systematic, accurate approximations for the dispersion relation of the nonlinear Klein-Gordon equation without special functions.

Findings

Analytical expressions for dispersion relations in strong nonlinear regimes

Method outperforms existing approaches in accuracy and simplicity

Applicable to systematic approximations of nonlinear wave equations

Abstract

We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the Linear Delta Expansion. All the results obtained in this article are fully analytical, never involve the use of special functions, and can be used to obtain systematic approximations to the exact results to any desired degree of accuracy. We compare our findings with similar results in the literature and show that our approach leads to better and simpler results.