Summary:
Solitons are some remarkable solutions of non linear differential equations that bare particle-like properties : they have a finite energy, a characteristic velocity of propagation and maintain their structures when two of them collide. The first equations that solitons appeared as solutions, were some non linear two dimensional differential equations of hydrodynamics, like the Korteweg-de Vries equation. In 1960, a method for solving those was developed, the Inverse Scattering Method(ISM). In the late 1970s the ISM was extended to General Relativity and offered a way to compute new solutions of the Einstein's field equations. Given a metric that is a solution of the Einstein equation in empty space, the method produces new metrics that remain solutions of the same equations. The ISM can be applied to metrics that posses certain symmetries. Namely, it can be applied to metrics that depend on two coordinates only. Hence, the are two families of produced solutions, the time dependent and time independent. The latter leads to the known solutions of the Kerr and Schwarzschild metrics. The time dependent solutions produce metrics that are of cosmological interest.
