Equations of Geodesic Deviation and the Inverse Scattering Transform

Details Equations of Geodesic Deviation and the Inverse Scattering Transform Equations of Geodesic Deviation and the Inverse Scattering Transform

1998-08-17

arxiv.org/abs/solv-int/9808007v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

32 pages, LaTeX2e, to appear in "Relativity, Gravitation, Cosmology" (Nova Science Publishers, New York)

Scientific paper

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.

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