Resources for Gravitational Soliton (specially on the Belinski–Zakharov transform)

Question

Can someone provide some resources (books, notes, articles etc.) on Gravitational Soliton (specially on the Belinski–Zakharov transform)?

I've found only the following two reference from the Wikipedia references:

1. Belinskii, V.; Zakharov, V. $(1978)$. "Integration of the Einstein Equations by Means of the Inverse Scattering Problem Technique and Construction of Exact Soliton Solutions". Sov. Phys. JETP. $48~(6):~985–994$. ISSN $0038-5646$.
2. Belinski, V.; Verdaguer, E. ($2001$). Gravitational Solitons. Cambridge Monographs on Mathematical Physics.

I'm searching for a few more.

NOTE: Wikipedia is saying,

The Belinski–Zakharov (inverse) transform is a nonlinear transformation that generates new exact solutions of the vacuum Einstein's field equation. It was developed by Vladimir Belinski and Vladimir Zakharov in $1978$.$^{[1]}$ The Belinski–Zakharov transform is a generalization of the inverse scattering transform. The solutions produced by this transform are called gravitational solitons (gravisolitons).

Answer 1

For the details of the Belinski–Zakharov transform I would recommend this paper of theirs, published the year following the one you already found:

• V.A. Belinskii, V.E. Zakharov, Stationary gravitational solitons with axial symmetry, Sov. Phys. JETP, 50(1), 1-9, (1979)

It can be hard to find PDFs of these papers, and honestly best place I have found to get them is on this conference website: zakharov75.itp.ac.ru/zve75/tt/publications.

Starting in the early 2000s their methods were generalized to higher dimensions, to reproduce Myers-Perry black holes, construct black saturn solutions, etc. Many of those newer papers have nice reviews of inverse scattering methods in GR (e.g. the Belinski–Zakharov transform). See for example

• arXiv:hep-th/0507250
• arXiv:hep-th/0701035

The book "Exact Solutions of Einstein's Field Equations" also tends to be a great reference for solution generating methods in GR.