S-functions, reductions and hodograph solutions of the
r-th dispersionless modified KP and Dym hierarchies
| dc.contributor.author | Mañas Baena, Manuel Enrique | |
| dc.date.accessioned | 2023-06-20T10:58:18Z | |
| dc.date.available | 2023-06-20T10:58:18Z | |
| dc.date.issued | 2004-11-12 | |
| dc.description | ©IOP Publishing. The author is in debt with Luis Martínez Alonso and Elena Medina, coauthors of [18], paper on which the present one is partially based. Partial economical support from Dirección General de Enseñanza Superior e Investigación Científica no BFM2002-01607 is also acknowledge. | |
| dc.description.abstract | We introduce an S-function formulation for the recently found rth dispersionless modified KP and rth dispersionless Dym hierarchies, giving also a connection of these S-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the S-function formulation leads to hodograph systems for the associated solutions. We consider also the connection of these reductions with those of the dispersionless KP hierarchy and with hydrodynamic-type systems. In particular, for the one-component and two-component reduction we derive, for both hierarchies, ample sets of examples of explicit solutions. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Dirección General de Enseñanza Superior e Investigación Científica | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/32555 | |
| dc.identifier.doi | 10.1088/0305-4470/37/46/007 | |
| dc.identifier.issn | 0305-4470 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1088/0305-4470/37/46/007 | |
| dc.identifier.relatedurl | http://iopscience.iop.org | |
| dc.identifier.relatedurl | http://arxiv.org/abs/nlin/0405028 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/51534 | |
| dc.issue.number | 46 | |
| dc.journal.title | Journal of physics A: Mathematical and general | |
| dc.language.iso | eng | |
| dc.page.final | 11221 | |
| dc.page.initial | 11191 | |
| dc.publisher | IOP Publishing | |
| dc.relation.projectID | BFM2002-01607 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Topological field-theory | |
| dc.subject.keyword | R-Matrix theory | |
| dc.subject.keyword | Integrable hierarchies | |
| dc.subject.keyword | Whitham hierarchy | |
| dc.subject.keyword | Additional symmetries | |
| dc.subject.keyword | Conformal-maps | |
| dc.subject.keyword | Dkp equation | |
| dc.subject.keyword | Tau-function | |
| dc.subject.keyword | Systems | |
| dc.subject.keyword | Deformations | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies | |
| dc.type | journal article | |
| dc.volume.number | 37 | |
| dcterms.references | [1] M. B laszak, Phys. Lett. A297 (2002) 191. [2] M. B laszak and B.M. Szablikowski, J. Phys. A: Math. Gen. 36 (2003) 12181. J. Phys. A: Math. Gen. 35 (2002) 10345. J. Phys. A: Math. Gen. 35 (2002) 10325 [3] B. Dubrovin, Nucl. Phys. B342 (1992) 627. B. Dubrovin and Y. Zhang, Commun. Math. Phys. 198 (1998) 311. [4] M. Dunajski, L. J. Mason and K. P. Tod, J. Geom. Phys. 37 (2001) 63. M. Dunajski and K. P. Tod, Phys. Lett. A 303 (2002) 253. [5] E.V. Ferapontov, D.A. Korotkin and V.A. Shramchenko, Quantum Grav. 19 (2002) L1- L6.M. Mañas and L. Mart´ınez Alonso, nlin.SI/020950 (2002), Theor. Math. Phys. 137 (2003) 1543, Phys. Lett. A320 (2004) 383. [6] E.V. Ferapontov, J. Phys. A: Math. Gen. 35 (2002) 6883-6892. E. V. Ferapontov and K. R. Khusnutdinova, On integrability of (2+1)-dimensional quasilinear systems, arXiv:nlin.SI/0305044 (2003). E. V. Ferapontov and K. R. Khusnutdinova, The characterization of two-component (2+1)- dimensional integrable systems of hydrodynamic type, arXiv:nlin.SI/0310021 (2003). [7] S. P. Tsarev, Iz. AN USSR Math 54 (1990) 1048. [8] J. Gibbons and S. P. Tsarev, Phys. Lett. A135 (1989) 167. Phys. Lett. A211 (1999) 263. [9] F. Guil, M. Mañas and L. Mart´ınez Alonso, J. Phys. A: Math. & Gen. 36 (2003) 4047. [10] F. Guil, M. Mañas and L. Martínez Alonso, J. Phys. A: Math. & Gen. 36 (2003) 6457. [11] Y. Kodama and J. Gibbons, Integrability of the dispersionless KP hierarchy. Proceedings of the 4th Workshop on Nonlinear and Turbulent Process in Physics, World Scientific, 1990. [12] Y. Kodama and J. Gibbons, Phys. Lett. A135 (1989) 167. [13] B. Konopelchenko and L. Martínez Alonso, Phys. Lett. A286 (2001) 161. J. Math. Phys. 43 (2002) 3807. Stud. Appl. Math. 109 (2002) 313. [14] B. Konopelchenko and A. Moro, J. Phys. A: Math. Gen. 37 (2004) L105. Integrable equations in nonlinear geometrical optics, arXiV:nlin.SI/0403051 (2004). [15] I. Krichever, Commun. Pure. Appl. Math. 47 (1994) 437. Commun. Math. Phys. 143 (1992) 415. [16] B. Kupershmidt, Commun. Math. Phys. 99 (1985) 51; J. Phys. A: Math. & Gen. 23 (1990) 871. [17] M. Mañas, On the r-th dispersionless Toda hierarchy I:Factorization problem, symmetries and some solutions, arXiV:nlin.SI/0404022 (2004). [18] M. Mañas, L. Martínez Alonso and E. Medina, J. Phys. A: Math. & Gen. 335 (2002) 401. [19] L.Martínez Alonso and M. Mañas, J. Math. Phys. 44 (2003) 3294. [20] K. Takasaki and T. Takebe, Lett. Math. Phys. 23 (1991) 205. [21] K. Takasaki and T. Takebe, Rev. Math. Phys. 7 (1995) 743. [22] K. Takasaki and T. Takebe, Int. J. Mod. Phys. 7, supp. 1B (1992) 889. K. Takasaki, Lett. Math. Phys.59 (2002), 157. [23] P. B. Wiegmann and A. Zabrodin Commun. Math. Phys. 213 (2000) 523. M. Mineev-Weinstein, P. B. Wiegmann and A. Zabrodin Phys. Rev. Lett. 84 (2000) 5106. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 0d5b5872-7553-4b33-b0e5-085ced5d8f42 | |
| relation.isAuthorOfPublication.latestForDiscovery | 0d5b5872-7553-4b33-b0e5-085ced5d8f42 |
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