Equations of Geodesic Deviation and the Inverse Scattering Transform
  Solutions of equations of geodesic deviation in three- and four- dimensional spaces obtained by the inverse scattering transform are considered. It is shown that in the case of three-dimensional space solutions of geodesic deviation equations are reduced to solutions of the well-known Zakharov-Shabat problem. In four- dimensional space system of geodesic deviation equations is associated with $3\times 3$ matrix Schr\"{o}dinger equation, and dependence on parameters defined by the nonlinear equations of three-wave interaction. 
Vadim V. Varlamov