Equations of Geodesic Deviation and the Inverse Scattering Transform
solv-int
2007-05-23 v2 General Relativity and Quantum Cosmology
Exactly Solvable and Integrable Systems
Abstract
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 matrix Schr\"{o}dinger equation, and dependence on parameters defined by the nonlinear equations of three-wave interaction.
Cite
@article{arxiv.solv-int/9808007,
title = {Equations of Geodesic Deviation and the Inverse Scattering Transform},
author = {Vadim V. Varlamov},
journal= {arXiv preprint arXiv:solv-int/9808007},
year = {2007}
}
Comments
32 pages, LaTeX2e, to appear in "Relativity, Gravitation, Cosmology" (Nova Science Publishers, New York)