Extended Harmonic Map Equations and the Chaotic Soliton Solutions

TL;DR

This paper extends the theory of harmonic maps to include soliton solutions of Euler's equations and investigates chaotic behaviors in these extended equations under specific conditions.

Contribution

It introduces an extension to harmonic map theory and explores soliton solutions and chaos in the resulting equations.

Findings

Soliton solutions of extended harmonic maps are identified.

Chaotic behaviors are observed in certain cases of the extended equations.

The study links metric and potential functions to chaotic dynamics.

Abstract

In this paper, the theory of harmonic maps is extended. The soliton or traveling wave solutions of Euler's equations of the extended harmonic maps are studied. In certain cases, the chaotic behaviors of these partial equations can be found for the particular case of the metrics and the potential functions of the extended harmonic equations.