Nonstationary one-soliton solutions of the vacuum Einstein equations with Alekseev's inverse scattering technique

Soliton solutions with real poles in the Alekseev formulation of the inverse-scattering method

“…For complex poles, the vacuum N -pole solitons in the Alekseev formalism are equivalent to 2N -pole solitons in the BZ formalism [5,8,10,11], although it may be noted that different spectral planes are adopted in the two formalisms. In order for the metric to be real, it is necessary that any complex pole in the BZ approach must be accompanied by its complex conjugate as another pole.…”