ON THE PROLONGATION STRUCTURE OF ERNST EQUATION |
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Authors: | GUO Han-ying WU Ke HSIAN Yan-yu WANG Shi-kun |
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Institution: | 1. Institute of Theoretical Physics, Academia Sinica P. O. Box 2735, Beijing, China;
2. Beijing Observatory, Academia Sinica P. O. Box 2727, Beijing, CHINA;
3. Institute of Applied Mathematics, Academia Sinica P. O. Box 300, Beijing, CHINA |
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Abstract: | An SL(2R) ×R1(l) prolongation structure of Ernst equation with a real parameter l and the corresponding Riccati equation as well as a pair of linear equations which are in principle equivalent to the inverse scattering problem due to Belinsky and Zakharov are obtained by solving the fundamental equation for the prolongation structure. A necessary condition which should be satisfied by the Bäcklund transformations is pfesented in terms of prolongation structure. And it is indicated that in the, case of Ernst equation the Harrison transformation, Neugebauer transformations and other available Bäcklund transformations as well as Belinsky-Zakharov's Riemann transformation, i.e., the homogeneous Hilbertproblem (HHP), would be covered by this condition. |
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