Generating quadrilateral and circular lattices in KP theory
| dc.contributor.author | Doliwa, Adam | |
| dc.contributor.author | Mañas Baena, Manuel Enrique | |
| dc.contributor.author | Martínez Alonso, Luis | |
| dc.date.accessioned | 2023-06-20T20:09:30Z | |
| dc.date.available | 2023-06-20T20:09:30Z | |
| dc.date.issued | 1999-11-08 | |
| dc.description | ©Physics letters A. | |
| dc.description.abstract | The bilinear equations of the N-component KP and BKP hierarchies and a corresponding extended Miwa transformation allow us to generate quadrilateral and circular lattices from conjugate and orthogonal nets, respectively. The main geometrical objects are expressed in terms of Baker functions. | |
| 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/32535 | |
| dc.identifier.doi | 10.1016/S0375-9601(99)00579-4 | |
| dc.identifier.issn | 0375-9601 | |
| dc.identifier.officialurl | http://dx.doi.org/ 10.1016/S0375-9601(99)00579-4 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.relatedurl | http://arxiv.org/abs/solv-int/9810012 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59707 | |
| dc.issue.number | 4-may | |
| dc.journal.title | Physics letters A | |
| dc.language.iso | eng | |
| dc.page.final | 343 | |
| dc.page.initial | 330 | |
| dc.publisher | Elsevier | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Discrete soliton-equations | |
| dc.subject.keyword | Ribaucour transformations | |
| dc.subject.keyword | Lame equations | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Generating quadrilateral and circular lattices in KP theory | |
| dc.type | journal article | |
| dc.volume.number | 262 | |
| dcterms.references | [1] L. Bianchi, Lezioni di Geometria Differenziale, 3-a ed., Zanichelli, Bologna (1924). [2] A. Bobenko, in Symmetries and Integrability of Difference Equations II, P. Clarkson and F. Nijhoff (eds.), Cambridge University Press, Cambridge (1997). [3] L. V. Bogdanov and B. G. Konopelchenko, J. Math. Phys. 39 (1998) 4701. [4] J. Ciéslínski, A. Doliwa and P. M. Santini, Phys. Lett. A235 (1997) 480. [5] G. Darboux, Le¸cons sur la théorie générale des surfaces IV, GauthierVillars, Paris (1896) Reprinted by Chelsea Publishing Company, New York (1972). [6] G. Darboux, Le¸cons 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). [7] E. Date, M. Jimbo, M. Kashiwara, and T. Miwa, J. Phys. Soc. Japan 50 (1981) 3806. [8] E. Date, M. Jimbo, M. Kashiwara and T. Miwa, Physica D4 (1982) 343. [9] E. Date, M. Jimbo and T. Miwa, J. Phys. Soc. Japan 51 (1982) 4116, 4125; 52 (1983) 388, 761, 766. [10] M. A. Demoulin, Comp. Rend. Acad. Sci. Paris 150 (1910) 156. [11] A. Doliwa, Quadratic reductions of quadrilateral lattices, solv-int/9802011. [12] A. Doliwa, S. V. Manakov and P. M. Santini, ¯∂-Reductions of the Multidimensional Quadrilateral Lattice I: the Multidimensional Circular Lattice. Commun. Math. Phys. (in press). [13] A. Doliwa, M. Mañas, L. Martínez Alonso, E. Medina and P. M. Santini, Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets, solv-int/9803015. [14] A. Doliwa and P. M. Santini, Phys. Lett. A 233 (1997) 365. [15] A. Doliwa, P. M. Santini and M. Mañas, Transformations for Quadrilateral Lattices, solv- int/9712017. [16] L. P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces, Ginn and Co., Boston (1909). [17] L. P. Eisenhart, Trans. Amer. Math. Soc. 18 (1917) 111. [18] L. P. Eisenhart, Transformations of Surfaces, Princeton University Press, Princeton (1923). Reprinted by Chelsea Publishing Company, New York (1962). [19] E. I. Ganzha, On completeness of the Ribaucour transformations for triply orthogonal curvilinear coordinate systems in R 3 , solv-int/9606002. [20] E. I. Ganzha and S. P. Tsarev, On superposition of the autoBäcklund transformations for (2+1)-dimensional integrable systems, solv-int/9606003. [21] R. Hirota, J. Phys. Soc. Japan 50 (1981) 3785. [22] H. Jonas, Berl. Math. Ges. Ber. Sitzungsber. 14 (1915) 96. [23] V. G. Kac and J. van de Leur, in Important Developments in Soliton Theory, edited by A. S. Fokas and V. E. Zakharov (Springer, Berlin, 1993) p. 302. [24] B. G. Konopelchenko and W. K. Schief, Three-dimensional Integrable Lattices in Euclidean Space: Conjugacy and Orthogonality, Preprint University of New South Wales (1997). [25] G. Lamé, Le¸cons sur la théorie des coordenées curvilignes et leurs diverses applications, Mallet-Bachalier, Paris (1859). [26] L. Lévy, J. l’Ecole Polytecnique 56 (1886) 63. [27] Q. P. Liu and M. Mañas, Phys. Lett. A239 (1998) 159. [28] Q. P. Liu and M. Mañas, J. Phys. A: Math. & Gen. 31 (1998) L193. [29] Q. P. Liu and M. Mañas, Superposition Formulae for the Discrete Ribaucour Transformations of Circular Lattices, Phys. Lett. A (in press). [30] M. Mañas, A. Doliwa and P. M. Santini, Phys. Lett. A232 (1997) 365. [31] M. Mañas and L. Martinez Alonso, From Ramond Fermions to Lamé Equations for Orthogonal Curvilinear Coordinates, Phys. Lett. B. (in press), solv-int/9805010. [32] R. R. Martin, in The Mathematics of Surfaces, J. Gregory (ed.), Claredon Press, Oxford (1986). [33] T. Miwa, Proc. Japan Acad. A58 (1982) 9. [34] A. W. Nutborne, in The Mathematics of Surfaces, J. Gregory (ed.), Claredon Press, Oxford (1986). [35] A. Ribaucour, Comp. Rend. Acad. Sci. Paris 74 (1872) 1489. [36] M. Sato, RIMS Kokyuroku 439 (1981) 30; in Theta Functions–Bowdoin 1987. Part 1 Proc. Sympos. Pure Maths. 49, part 1, 51, AMS (1989) Providence. [37] R. Sauer, Differenzengeometrie, Springer-Verlag, Berlin (1970) [38] G. Segal and G. Wilson, Publ. Math. I. H. E. S. 61, 5, 1985. [39] V. E. Zakharov, On Integrability of the Equations Describing NOrthogonal Curvilinear Coordinate Systems and Hamiltonian Integrable Systems of Hydrodynamic Type I: Integration of the Lam´e Equations Preprint (1996). [40] V. E. Zakharov and S. V. Manakov, Func. Anal. Appl. 19 (1985) 11. | |
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