Relationship Between Solitonic Solutions of Five-Dimensional Einstein Equations

TL;DR

This paper explores the connection between two solution-generating techniques, inverse scattering and Bäcklund transformation, for five-dimensional Einstein equations, showing that two-solitonic solutions from both methods are related.

Contribution

It establishes a direct relation between inverse scattering and Bäcklund transformation methods for generating solitonic solutions in five-dimensional Einstein equations.

Findings

Two-solitonic solutions from Bäcklund are contained within inverse scattering solutions.

The paper clarifies the relationship between two prominent solution-generating methods.

It enhances understanding of soliton solutions in higher-dimensional gravity theories.

Abstract

We give the relation between the solutions generated by the inverse scattering method and the B\"acklund transformation applied to the vacuum five-dimensional Einstein equations. In particular, we show that the two-solitonic solutions generated from an arbitrary diagonal seed by the B\"acklund transformation are contained within those generated from the same seed by the inverse scattering method.