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Dispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical δ̅ -dressing method

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dc.contributor.authorKonopelchenko, Boris
dc.contributor.authorMartínez Alonso, Luis
dc.date.accessioned2023-06-20T20:12:15Z
dc.date.available2023-06-20T20:12:15Z
dc.date.issued2002-07
dc.description©2002 American Institute of Physics. This work has been done in the framework of Grant No. INTAS-99-1782. B.K. was supported in part by the grant COFIN 2000 ‘‘Sintesi.’’ L.M.A. has supported in part by CICYT Proyecto No. PB98-0821. B.K. is grateful to the Departamento de Fisica Teorica II Universidad Complutense for kind hospitality during which this paper was basically written.
dc.description.abstractThe quasiclassical limit of the scalar nonlocal δ̅ -problem is derived and a quasiclassical version of the δ̅-dressing method is presented. Dispersionless Kadomtsev– Petviashvili (KP), modified KP, and dispersionless two- dimensional Toda lattice (2DTL) hierarchies are discussed as illustrative examples. It is shown that the universal Whitham hierarchy is nothing but the ring of symmetries for the quasiclassical δ̅-problem. The reduction problem is discussed and, in particular, the d2DTL equation of B type is derived.
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/34420
dc.identifier.doi10.1063/1.1481545
dc.identifier.issn0022-2488
dc.identifier.officialurlhttp://dx.doi.org/10.1063/1.1481545
dc.identifier.relatedurlhttp://scitation.aip.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/59825
dc.issue.number7
dc.journal.titleJournal of mathematical physics
dc.language.isoeng
dc.page.final3823
dc.page.initial3807
dc.publisherAmerican Institute of Physics
dc.relation.projectIDINTAS-99-1782
dc.relation.projectID2000 "Sintesi"
dc.relation.projectIDPB98-0821
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordKorteweg-devries equation
dc.subject.keywordTopological field-theory
dc.subject.keywordQuasi-classical limit
dc.subject.keywordConformal-maps
dc.subject.keywordKp hierarchy
dc.subject.keywordSystems
dc.subject.keywordModels
dc.subject.keywordDimensions
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleDispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical δ̅ -dressing method
dc.typejournal article
dc.volume.number43
dcterms.references1. B. A. Kuperschmidt and Yu. I. Manin, Funct. Anal. Appl. 11, 31 (1977); 17, 25 (1978). 2.V. E. Zakharov, Funct. Anal. Appl., 14, 89 (1980); Physica D 3, 193 (1981). 3. P. D. Lax and C. D. Levermore, Commun. Pure Appl. Math. 36, 253 (1983); 36, 571 (1983); 36, 809 (1983). 4. I. M. Krichever, Funct. Anal. Appl. 22, 37 (1988). 5. Y. Kodama, Phys. Lett. A 129, 223 (1988); 147, 477 (1990). 6. B. A. Dubrovin and S. P. Novikov, Russ. Math. Surveys 44, 35 (1989). 7. K. Takasaki and T. Takebe, Int. J. Mod. Phys. A 1, 889 (1992). 8. I. M. Krichever, Commun. Pure Appl. Math. 47, 437 (1994). 9. Singular Limits of Dispersive Waves, edited by N. M. Ercolani et al., Nato Adv. Sci. Inst. Ser. B Phys., Vol. 320 (Plenum, New York, 1994). 10. V. E. Zakharov, in Ref. 9, pp. 165–174. 11. K. Takasaki and T. Takebe, Rev. Math. Phys. 7, 743 (1995). 12. R. Carroll and Y. Kodama, J. Phys. A 28, 6373 (1995). 13. S. Jin, C. D. Levermore, and D. W. McLaughlin, Commun. Pure Appl. Math. 52, 613 (1999). 14. I. M. Krichever, Commun. Math. Phys. 143, 415 (1992). 15. B. A. Dubrovin, Commun. Math. Phys. 145, 195 (1992); B. A. Dubrovin, Nucl. Phys. B 379, 627 (1992); B. A. Dubrovin and Y. Zhang, Commun. Math. Phys. 198, 311 (1998). 16. S. Aoyama and Y. Kodama, Commun. Math. Phys. 182, 185 (1996). 17. Y. Gibbons and S. P. Tsarev, Phys. Lett. A 258, 263 (1999). 18. P. B. Wiegmann and A. Zabrodin, Commun. Math. Phys. 213, 523 (2000); M. Mineev- Weinstein P. B. Wiegmann, and A. Zabrodin, Phys. Rev. Lett. 84, 5106 (2000). 19. V. V. Geogdzhaev, Teor. Mat. Fiz. 73, 255 (1987). 20. B. Konopelchenko, L. Martinez Alonso, and O. Ragnisco, ‘‘δ̅-approach to the dispersionless KP hierarchy,’’ Talk given at SIDE IV Meeting, Tokyo, November 2000. 21. L. V. Ahlfors, Lectures on Quasi-conformal Mappings (Van Nostrand, Princeton, 1966). 22. O. Letho and K. I. Virtanen, Quasiconformal Mappings in the Plane (Springer, Berlin, 1973). 23. L. Bers, Bull. Am. Math. Soc. 83, 1083 (1977). 24. V. E. Zakharov and S. V. Manakov, Funct. Anal. Appl. 19, 89 (1985). 25.V. E. Zakharov, in Inverse Problems in Action, edited by P. S. Sabatier (Springer, Berlin, 1990), p. 602. 26. B. G. Konopelchenko, Solitons in Multidimensions (World Scientific, Singapore, 1993). 27. I. N. Vekua, Generalized Analytic Functions (Pergamon, Oxford, 1962). 28. V. P. Maslov, Complex WKB Method for Nonlinear Equations (Nauka, Moscow, 1977). 29. B. A. Kuperschmidt, J. Phys. A 23, 871 (1990). 30. K. Takasaki, Lett. Math. Phys. 28, 177 (1993). 31. M. Jimbo and T. Miwa, Publ. RIMS, Kyoto Univ. 19, 943 (1983). 32. B. G. Konopelchenko and V. G. Dubrovsky, Phys. Lett. 102A, 15 (1984).
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