Vectorial Ribaucour transformations for the Lame equations
| dc.contributor.author | Liu, Q. P. | |
| dc.contributor.author | Mañas Baena, Manuel Enrique | |
| dc.date.accessioned | 2023-06-20T20:09:16Z | |
| dc.date.available | 2023-06-20T20:09:16Z | |
| dc.date.issued | 1998-03-13 | |
| dc.description | ©IOP Publishing LTD. M. M. would like to thank several conversations with A. Doliwa and P. M. Santini. In particular, A. Doliwa’s historical remarks were quite useful. | |
| dc.description.abstract | The vectorial extension of the Ribaucour transformation for the Lame equations bf orthogonal conjugate nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which follows the permutability of the vectorial Ribaucour transformations. Finally, as an example we apply the vectorial Ribaucour transformation to the Cartesian background. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/32499 | |
| dc.identifier.doi | 10.1088/0305-4470/31/10/003 | |
| dc.identifier.issn | 0305-4470 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1088/0305-4470/31/10/003 | |
| dc.identifier.relatedurl | http://iopscience.iop.org | |
| dc.identifier.relatedurl | http://arxiv.org/abs/solv-int/9710014 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59696 | |
| dc.issue.number | 10 | |
| dc.journal.title | Journal of Physics A-Mathematical and General | |
| dc.language.iso | eng | |
| dc.page.final | L200 | |
| dc.page.initial | L193 | |
| dc.publisher | IOP Publishing LTD | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Vectorial Ribaucour transformations for the Lame equations | |
| dc.type | journal article | |
| dc.volume.number | 31 | |
| dcterms.references | [1] L. Bianchi, Rendi. Lincei 13 (1904) 361. [2] L. Bianchi, Lezioni di Geometria Differenziale, 3-a ed., Zanichelli, Bologna (1924). [3] G. Darboux, Leçons sur la théorie générale des surfaces IV, GauthierVillars, Paris (1896) Reprinted by Chelsea Publishing Company, New York (1972). [4] G. Darboux, Leçons sur les systèmes orthogonaux et les coordenées curvilignes (deuxième édition), Gauthier-Villars, Paris (1910) (the first edition was in 1897). Reprinted by Éditions Jacques Gabay, Sceaux (1993). [5] M. A. Demoulin, Comp. Rend. Acad. Sci. Paris 150 (1910) 156. [6] A. Doliwa, P. M. Santini and M. Mañas, Transformations for Quadrilateral Lattices, to appear (1997). [7] L. P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces, Ginn and Co., Boston (1909). [8] L. P. Eisenhart, Trans. Amer. Math. Soc. 18 (1917) 111. [9] L. P. Eisenhart, Transformations of Surfaces, Princeton University Press, Princeton (1923). Reprinted by Chelsea Publishing Company, New York (1962). [10] E. I. Ganzha and S. P. Tsarev, On superposition of the autoBäcklund transformations for (2+1)-dimensional integrable systems, solv-int/9606003. [11] H. Jonas, Berl. Math. Ges. Ber. Sitzungsber. 14 (1915) 96. [12] B. G. Konopelchenko and W. K. Schief, Lamé and Zakharov-Manakov systems: Combescure, Darboux and Bäcklund transformations, Preprint Applied Mathematics 93/9, University of New South Wales (1993). [13] G. Lamé, Le¸cons sur la théorie des oordenées curvilignes et leurs diverses applications, Mallet-Bachalier, Paris (1859). [14] M. Mañaas, A. Doliwa and P. M. Santini, Phys. Lett. 232 A (1997) 365. [15] A. Ribaucour, Comp. Rend. Acad. Sci. Paris 74 (1872) 1489. [16] W. K. Schief, Inv. Prob. 10 (1994) 1185. [17] S. P. Tsarev, Classical differential geometry and integrability of systems of hydrodynamic type, in Applications of analytic and geometrical methods to nonlinear differential equations, ed. P. A. Clarkson, Kluwer, Dortrecht (1993). [18] V. E. Zakharov, On Integrability of the Equations Describing NOrthogonal Curvilinear Coordinate Systems and Hamiltonian Integrable Systems of Hydrodynamic Type I: Integration of the Lamé Equations Preprint (1996). [19] V. E. Zakharov and S. V. Manakov, Func. Anal. Appl. 19 (1985) 11. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 0d5b5872-7553-4b33-b0e5-085ced5d8f42 | |
| relation.isAuthorOfPublication.latestForDiscovery | 0d5b5872-7553-4b33-b0e5-085ced5d8f42 |
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