KdV solitons in Einstein's vacuum field equations

Abstract

We present a metric for which Einstein's field equations in vacuum generate the Kortweg-de Vries (KdV) equation and thus its $N$-soliton solutions solve the vacuum equations. The metric of the one soliton solution has been investigated and is a non-singular, Lorentzian metric of type N in the Petrov classification.

6 pages, no figures