Cover -- Half-title -- Series-title -- Title -- Copyright -- Contents -- Preface -- 1 Inverse scattering technique in gravity -- 1.1 Outline of the ISM -- 1.1.1 The method -- 1.1.2 Generalization and examples -- 1.2 The integrable ansatz in general relativity -- 1.3 The integration scheme -- 1.4 Construction of the n-soliton solution -- 1.4.1 The physical metric components g -- 1.4.2 The physical metric component f -- 1.5 Multidimensional spacetime -- 2 General properties of gravitational solitons -- 2.1 The simple and double solitons -- 2.1.1 Pole fusion -- 2.2 Diagonal background metrics -- 2.3 Topological properties -- 2.3.1 Gravisolitons and antigravisolitons -- 2.3.2 The gravibreather solution -- 3 Einstein-Maxwell fields -- 3.1 The Einstein-Maxwell field equations -- 3.2 The spectral problem for Einstein-Maxwell fields -- 3.3 The components g and the potentials A -- 3.3.1 The n-soliton solution of the spectral problem -- 3.3.2 The matrix X -- 3.3.3 Verification of the constraints -- 3.3.4 Summary of prescriptions -- 3.4 The metric component f -- 3.5 Einstein-Maxwell breathers -- 4 Cosmology: diagonal metrics from Kasner -- 4.1 Anisotropic and inhomogeneous cosmologies -- 4.2 Kasner background -- 4.3 Geometrical characterization of diagonal metrics -- 4.3.1 Riemann tensor and Petrov classification -- 4.3.2 Optical scalars -- 4.3.3 Superenergy tensor -- 4.4 Soliton solutions in canonical coordinates -- 4.4.1 Generalized soliton solutions -- 4.5 Solutions with real poles -- 4.5.1 Generation of Bianchi models from Kasner -- 4.5.2 Pulse waves -- 4.5.3 Cosolitons -- 4.6 Solutions with complex poles -- 4.6.1 Composite universes -- 4.6.2 Cosolitons -- 4.6.3 Soliton collision -- 5 Cosmology: nondiagonal metrics and perturbed FLRW -- 5.1 Nondiagonal metrics -- 5.1.1 Solutions with real poles -- 5.1.2 Solutions with complex poles.

5.2 Bianchi II backgrounds -- 5.3 Collision of pulse waves and soliton waves -- 5.4 Solitons on FLRW backgrounds -- 5.4.1 Solitons on vacuum FLRW backgrounds -- 5.4.2 Solitons with a stiff perfect fluid on FLRW -- 5.4.3 The Kaluza-Klein ansatz and theories with scalar fields -- 5.4.4 Solitons on radiative, and other, FLRW backgrounds -- 6 Cylindrical symmetry -- 6.1 Cylindrically symmetric spacetimes -- 6.2 Einstein-Rosen soliton metrics -- 6.2.1 Solutions with one pole -- 6.2.2 Cosolitons with one pole -- 6.2.3 Solitons with two opposite poles -- 6.2.4 Cosolitons with two opposite poles -- 6.3 Two polarization waves and Faraday rotation -- 6.3.1 One real pole -- 6.3.2 Two complex poles -- 6.3.3 Two double complex poles -- 7 Plane waves and colliding plane waves -- 7.1 Overview -- 7.2 Plane waves -- 7.2.1 The plane-wave spacetime -- 7.2.2 Focusing of geodesics -- 7.2.3 Plane-wave soliton solutions -- 7.3 Colliding plane waves -- 7.3.1 The matching conditions -- 7.3.2 Collinear polarization waves: generalized soliton solutions -- 7.3.3 Geometry of the colliding waves spacetime -- 7.3.4 Noncollinear polarization waves: nondiagonal metrics -- 8 Axial symmetry -- 8.1 The integration scheme -- 8.2 General n-soliton solution -- 8.3 The Kerr and Schwarzschild metrics -- 8.4 Asymptotic flatness of the solution -- 8.5 Generalized soliton solutions of the Weyl class -- 8.5.1 Generalized one-soliton solutions -- 8.5.2 Generalized two-soliton solutions -- 8.6 Tomimatsu-Sato solution -- Bibliography -- Index.