Effective chiral model of a plane-symmetric gravitational field:   properties and exact solutions
  An effective chiral model of a plane-symmetric gravitational field is considered. Isometries of the target space of the model are described and exact solutions corresponding to the isometric ansatz method are obtained. New exact solutions are found using the method of functional parameters. The solutions obtained are B\"acklund transforms of solutions of the d'Alembert equation to those of the Einstein equations. 
Victor M. Zhuravlev, Serguey V. Chervon and Dmitriy Yu. Shabalkin