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Integrable deformations of algebraic curves

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dc.contributor.authorKodama, Y.
dc.contributor.authorKonopelchenko, Boris
dc.contributor.authorMartínez Alonso, Luis
dc.date.accessioned2023-06-20T11:03:11Z
dc.date.available2023-06-20T11:03:11Z
dc.date.issued2005-07
dc.description©2005 Springer Science+Business Media, Inc. One of the authors (L. M. A.) thanks the members of the Physics Department of Lecce University for their warm hospitality. This work was supported in part by the DGCYT (Project No. BFM2002-01607), COFIN (Grant 2002 “Sintesi”), and the National Science Foundation (Grant No. DMS-0404931).
dc.description.abstractWe present a general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations. We emphasize the use of several types of dynamical variables: branches, power sums, and potentials.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipDGCYT
dc.description.sponsorshipCOFIN
dc.description.sponsorshipNational Science Foundation
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/34327
dc.identifier.doi10.1007/s11232-005-0123-9
dc.identifier.issn0040-5779
dc.identifier.officialurlhttp://dx.doi.org/10.1007/s11232-005-0123-9
dc.identifier.relatedurlhttp://link.springer.com
dc.identifier.relatedurlhttp://arxiv.org/abs/nlin/0409063
dc.identifier.urihttps://hdl.handle.net/20.500.14352/51649
dc.issue.number1
dc.journal.titleTheoretical and mathematical physics
dc.language.isoeng
dc.page.final967
dc.page.initial961
dc.publisherSpringer
dc.relation.projectIDBFM2002-01607
dc.relation.projectIDGrant 2002 “Sintesi”
dc.relation.projectIDDMS-0404931
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordAlgebraic curves
dc.subject.keywordIntegrable systems
dc.subject.keywordLenard relations
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleIntegrable deformations of algebraic curves
dc.typejournal article
dc.volume.number144
dcterms.references1. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984); E. D. Belokolos, A. I. Bobenko, V. Z. Enol´ski, A. R. Its, and V. B. Matveev, Algebro-Geometric Approach to Nonlinear Integrable Equations, Springer, Berlin (1994); B. A. Dubrovin and S. P. Novikov, Russ. Math. Surveys, 44, No. 6, 35 (1989); H. Flaschka, M. G. Forest, and D. W. Mclauglin, Comm. Pure Appl. Math., 33, 739 (1980); B. A. Dubrovin, Comm. Math. Phys., 145, 415 (1992). 2. I. M. Krichever, Funct. Anal. Appl., 22, 200 (1988); Comm. Pure Appl. Math., 47, 437 (1994). 3. Y. Kodama and B. G. Konopelchenko, J. Phys. A, 35, L489-L500 (2002); “Deformations of plane algebraic curves and integrable systems of hydrodynamic type,” in: Nonlinear Physics: Theory and Experiment II (Proc. Intl. Workshop, Gallipoli, Lecce, Italy, 2002, M. J. Ablowitz, M. Boiti, F. Pempinelli, and B. Prinari, eds.), World Scientific, River Edge, N. J. (2003), p. 234. 4. B. G. Konopelchenko and L. Mart´ınez Alonso, J. Phys. A, 37, 7859 (2004). 5. C. L. Siegel, Topics in Complex Function Theory, Vol. 1, Elliptic Functions and Uniformization Theory, Wiley, New York (1969). 6. R. Y. Walker, Algebraic Curves, Springer, Berlin (1978). 7. S. S. Abhyankar, Algebraic Geometry for Scientists and Engineers (Math. Surveys and Monographs, Vol. 35), Amer. Math. Soc., Providence, R. I. (1990). 8. B. L. van der Waerden, Algebra, Vol. 1, Springer, Berlin (1991). 9. L. Redei, Introduction to Algebra, Vol. 1, Pergamon, Oxford (1967). 10. I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon, Oxford (1979). 11. L. Schwartz, Analyse mathématique, Vol. 2, Hermann, Paris (1967)
dspace.entity.typePublication
relation.isAuthorOfPublication896aafc0-9740-4609-bc38-829f249a0d2b
relation.isAuthorOfPublication.latestForDiscovery896aafc0-9740-4609-bc38-829f249a0d2b

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