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δ̅-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy

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dc.contributor.authorKonopelchenko, Boris
dc.contributor.authorMartínez Alonso, Luis
dc.date.accessioned2023-06-20T20:12:17Z
dc.date.available2023-06-20T20:12:17Z
dc.date.issued2001-07-22
dc.description©2001 Elsevier Science B.V. All rights reserved. We would like to thank Prof. E. Medina for carrying out the computer calculation of the coefficients in the second example of Section 4. B.K. is supported in part by COFIN 2000 “Sintesi” and L.M.A. by proyecto PB98-0821.
dc.description.abstractIt is shown that the dispersionless scalar integrable hierarchies and, in general, the universal hitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane. Examples of deformations of quasiconformal mappings associated with explicit solutions of the dispersionless KP hierarchy are presented.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipCOFIN
dc.description.sponsorshipCICYT
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/34452
dc.identifier.doi10.1016/S0375-9601(01)00395-4
dc.identifier.issn0375-9601
dc.identifier.officialurlhttp://dx.doi.org/10.1016/S0375-9601(01)00395-4
dc.identifier.relatedurlhttp://www.sciencedirect.com
dc.identifier.relatedurlhttp://arxiv.org/abs/nlin/0103015
dc.identifier.urihttps://hdl.handle.net/20.500.14352/59827
dc.issue.number2-mar
dc.journal.titlePhysics letters A
dc.language.isoeng
dc.page.final166
dc.page.initial161
dc.publisherElsevier
dc.relation.projectID2000 “Sintesi”
dc.relation.projectIDPB98-0821.
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordRteweg-devries equation
dc.subject.keywordSmall dispersion limit
dc.subject.keywordConformal-maps
dc.subject.keywordModels
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleδ̅-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy
dc.typejournal article
dc.volume.number286
dcterms.references[1] V.E. Zakharov, Funkt. Anal. Prilozh. 14 (1980) 89; V.E. Zakharov, Physica 3D (1981) 193. [2] P.D. Lax, C.D. Levermore, Comm. Pure Appl. Math. 36 (1983) 253, 571, 809. [3] Y. Kodama, Phys. Lett. 129A (1988) 223; Y. Kodama, Phys. Lett. 147A (1990) 477. [4] I.M. Krichever, Funkt. Anal. Prilozh. 22 (1988) 37; I.M. Krichever, Comm. Pure Appl. Math. 47 (1994) 437. [5] B.A. Dubrovin, S.P. Novikov, Russian Math. Surveys 44 (1989) 35. [6] K. Takasaki, T. Takebe, Int. J. Mod. Phys. A Suppl. 1B (1992) 889; K. Takasaki, T. Takebe, Rev. Math. Phys. 7 (1995) 743. [7] N.M. Ercolani et al. (Eds.), Singular Limits of Dispersive Waves, NATO Adv. Sci. Inst. Ser. B Phys., Vol. 320, Plenum, New York, 1994. [8] I.M. Krichever, Comm. Math. Phys. 143 (1992) 415. [9] B.A. Dubrovin, Comm. Math. Phys. 145 (1992) 195; B.A. Dubrovin, Y. Zhang, Comm. Math. Phys. 198 (1998) 311. [10] Y. Kodama, solv-int/9709012. [11] J. Gibbons, S.P. Tsarev, Phys. Lett. 258A (1999) 263. [12] P.B. Wiegmann, A. Zabrodin, Comm. Math. Phys 213 (2000) 523. [13] L.V. Ahlfors, Lectures on Quasi-Conformal Mappings, D. Van Nostrand, Princeton, 1966. [14] Q. Lehto, K.I. Virtanen, Quasiconformal Mappings in the Plane, Springer, Berlin, 1973. [15] B. Bojarski, Sympos. Math. XVIII (1976) 485. [16] T. Iwaniec, Sympos. Math. XVIII (1976) 501. [17] B. Konopelchenko, L. Martínez Alonso, O. Ragnisco, in: SIDE IV Workshop, Tokyo, 2000. [18] B. Konopelchenko, L. Martínez Alonso, Dispersionless scalar integrable hierarchies, universal Whitham hierarchy and the quasiclassical ∂¯-dressing method, submitted. [19] I.N. Vekua, Generalized Analytic Functions, Pergamon Press, Oxford, 1962. [20] J. Lawrynowicz, Quasiconformal Mappings in the Plane: Parametric Methods, Lecture Notes in Math., Vol. 978, Springer, Berlin, 1983. [21] S.L. Kruskal, Quasiconformal Mappings and Riemann Surfaces, Wiley, New York, 1979. [22] O. Lehto, Univalent Functions and Teichmüller Spaces, Springer, Berlin, 1987. [23] L. Carleson, T.W. Gamelin, Complex Dynamics, Springer, Berlin, 1993.
dspace.entity.typePublication
relation.isAuthorOfPublication896aafc0-9740-4609-bc38-829f249a0d2b
relation.isAuthorOfPublication.latestForDiscovery896aafc0-9740-4609-bc38-829f249a0d2b

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