Integration of the Einstein equations by the method of the inverse scattering problem and calculation of exact soliton solutions
Abstract
An application of a modified method of the inverse scattering problem to the integration of the gravitationalfield equations is described for the case where the metric tensor is a function of only the time coordinate and one space coordinate. Simplified one and twosoliton solutions are calculated in explicit form. A procedure is outlined for obtaining solutions in the general case where the solution contains both a soliton and a nonsoliton component.
 Publication:

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki
 Pub Date:
 December 1978
 Bibcode:
 1978ZhETF..75.1953B
 Keywords:

 Einstein Equations;
 Gravitational Fields;
 Solitary Waves;
 Cauchy Integral Formula;
 Integral Equations;
 Matrices (Mathematics);
 Scattering Functions;
 Time Functions;
 Physics (General)