2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94451Solutions 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 Schrödinger equation, and dependence on parameters defined by the nonlinear equations of three-wave interaction.32 pages, LaTeX2e, to appear in "Relativity, Gravitation, Cosmology" (Nova Science Publishers, New York)Exactly Solvable and Integrable SystemsGeneral Relativity and Quantum Cosmologytext