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Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type

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dc.contributor.authorMartínez Alonso, Luis
dc.contributor.authorShabat, A. B.
dc.date.accessioned2023-06-20T20:12:14Z
dc.date.available2023-06-20T20:12:14Z
dc.date.issued2002-07-22
dc.description©2002 Elsevier Science B.V. All rights reserved. A.B. Shabat was supported by the Russian Foundation for Basic Research (Grant Nos. 96-15-96093 and 98-01- 01161), INTAS (Grant No. 99-1782) and a Rotschild professorship. L. Martı́nez Alonso was supported by the Fundación Banco Bilbao Vizcaya Argentaria. Both authors wish to thank the organizers of the program Integrable Systems at the Newton Institute of Cambridge University for their warm hospitality.
dc.description.abstractA hierarchy of infinite-dimensional systems of hydrodynamic type is considered and a general scheme for classifying its reductions is provided. Wide families of integrable systems including, in particular, those associated with energy-dependent spectral problems of Schrodinger type, are characterized as reductions of this hierarchy. N-phase type reductions and their corresponding Dubrovin equations are analyzed. A symmetry transformation connecting different classes of reductions is formulated.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipRussian Foundation for Basic Research
dc.description.sponsorshipINTAS
dc.description.sponsorshipFundación Banco Bilbao Vizcaya Argentaria
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/34413
dc.identifier.doi10.1016/S0375-9601(02)00662-X
dc.identifier.issn0375-9601
dc.identifier.officialurlhttp://dx.doi.org/10.1016/S0375-9601(02)00662-X
dc.identifier.relatedurlhttp://www.sciencedirect.com
dc.identifier.relatedurlhttp://arxiv.org/abs/nlin/0202008#
dc.identifier.urihttps://hdl.handle.net/20.500.14352/59824
dc.issue.number1
dc.journal.titlePhysics letters A
dc.language.isoeng
dc.page.final64
dc.page.initial58
dc.publisherElsevier
dc.relation.projectID96-15-96093
dc.relation.projectID98-01- 01161
dc.relation.projectID99-1782
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordIntegrable hierarchies
dc.subject.keywordBenney equations
dc.subject.keywordKp hierarchy
dc.subject.keywordDispersionless
dc.subject.keywordReductions
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleEnergy-dependent potentials revisited: a universal hierarchy of hydrodynamic type
dc.typejournal article
dc.volume.number300
dcterms.references[1] B.A Dubrovin, V.B Matveev, S.P Novikov Usp. Mat. Nauk, 31 (1) (1976), p. 55 [2] V.G Mikhalev Functional Anal. Appl., 26 (2) (1992), p. 140 [3] M Jaulent, I Miodek Lett. Math. Phys., 1 (1976), p. 243 M Jaulent, I Miodek Lett. Nuovo Cimento, 20 (1977), p. 655 [4] L Martı́nez Alonso J. Math. Phys., 21 (1980), p. 2342 [5] M Antonowicz, A.P Fordy Physica D, 28 (1987), p. 345 [6] M Mañas, L Martı́nez Alonso, E Medina [7] A.N.W Hone Phys. Lett. A, 249 (1998), p. 46 [8] B Konopelchenko, L Martı́nez Alonso, E Medina J. Phys. A: Math. Gen. 32, 3621 (1999). [9] A.B Shabat Theor. Math. Phys., 121 (1) (1999), p. 1397 [10] I.M Krichever Commun. Pure. Appl. Math., 47 (1992), p. 437 I.M Krichever Commun. Math. Phys., 143 (1992), p. 415 [11] T Takasaky, T Takebe Int. J. Mod. Phys. A, 7 (Suppl. 1B) (1992), p. 889, Rev. Math. Phys., 7 (1995), p. 743 [12] Y Kodama Phys. Lett. A, 129 (1988), p. 223 [13] Y Kodama, J Gibbons Phys. Lett. A, 135 (1989), p. 167 [14] J Gibbons, S.P TsarevPhys. Lett. A, 211 (1996), p. 19 [15]J Gibbons, S.P Tsarev Phys. Lett. A, 258 (1999), p. 263 [16] M Mañas, L Martı́nez Alonso, E Medina J. Phys. A, 35 (2002), p. 401 [17] E.V Ferapontov Phys. Lett. A, 158 (1991), p. 112
dspace.entity.typePublication
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relation.isAuthorOfPublication.latestForDiscovery896aafc0-9740-4609-bc38-829f249a0d2b

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