Soliton Solutions with Real Poles in the Alekseev formulation of the Inverse-Scattering method

TL;DR

This paper introduces a novel approach within Alekseev's inverse-scattering method that enables the construction of real-pole soliton solutions for the Ernst equations, including explicit solutions for the vacuum case.

Contribution

It presents a new technique for real-pole soliton solutions in Alekseev's framework, linking it with Belinskii-Zakharov solutions and providing explicit examples.

Findings

Explicit solutions for vacuum case using Minkowski seed metric

Relation established between Alekseev and Belinskii-Zakharov solutions

Method allows real-pole soliton solutions in the inverse-scattering framework

Abstract

A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the corresponding soliton solutions that can be constructed using the Belinskii-Zakharov inverse-scattering technique is determined.