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Towards a theory of differential constraints of a hydrodynamic hierarchy

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dc.contributor.authorMartínez Alonso, Luis
dc.contributor.authorShabat, A. B.
dc.date.accessioned2023-06-20T11:03:26Z
dc.date.available2023-06-20T11:03:26Z
dc.date.issued2003-05
dc.description©Atlantis Press. A B Shabat wish to thank A Ibort for his support during his stay as a visiting professor of the Carlos III University of Madrid. He also acknowledges the group of the Department of Theoretical Physics II of the Complutense University for their warm hospitality. L Martínez Alonso was partially supported by the DGCYT project BFM2002- 01607. A Shabat was partially supported by the RFFI project 01-01-00874 and Sc. Schools RF grant 06- 15-96093. Both authors are grateful to E Ferapontov for several useful and stimulating discussions.
dc.description.abstractWe present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative examples and new integrable models are exhibited.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipDGCYT
dc.description.sponsorshipRFFI
dc.description.sponsorshipSc. Schools RF
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/34387
dc.identifier.doi10.2991/jnmp.2003.10.2.6
dc.identifier.issn1402-9251
dc.identifier.officialurlhttp://dx.doi.org/10.2991/jnmp.2003.10.2.6
dc.identifier.relatedurlhttp://www.tandfonline.com
dc.identifier.relatedurlhttp://arxiv.org/abs/nlin/0310036
dc.identifier.urihttps://hdl.handle.net/20.500.14352/51655
dc.issue.number2
dc.journal.titleJournal of nonlinear mathematical physics
dc.language.isoeng
dc.page.final242
dc.page.initial229
dc.publisherAtlantis Press
dc.relation.projectIDBFM2002- 01607
dc.relation.projectID01-01-00874
dc.relation.projectID06- 15-96093
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordMathematics
dc.subject.keywordapplied
dc.subject.keywordPhysics
dc.subject.keywordmathematical
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleTowards a theory of differential constraints of a hydrodynamic hierarchy
dc.typejournal article
dc.volume.number10
dcterms.references[1] Rozdestvenskii B L and Sidorenko A D, On the Impossibility of “Gradient Catastrophe” for Weakly Nonlinear Systems, Comput. Math. & Math. Phys. 7 (1967), 1176–1179. [2] Dubrovin B A, Matveev V B and Novikov S P, Nonlinear Equations of Korteweg-de Vries Type, Finite-Band Linear Operators and Abelian Varieties, Usp. Mat. Nauk 31, Nr. 1 (1976), 55–136. [3] Mikhalev V G, Hamiltonian Formalism of Korteweg-de Vries- Type Hierarchies, Funct. Anal. Appl. 26, Nr. 2 (1992), 140–142. [4] Hone A N W, Reciprocal Transformations, Painlevé Property and Solutions of EnergyDependent Schr¨odinger Hierarchies, Phys. Lett. A249 (1998), 46–54. [5] Martinez Alonso L and Shabat A B, Energy-Dependent Potentials Revisited: A Universal Hierarchy of Hydrodynamic Type,Phys. Lett. A300 (2002), 58-64. [6] Liouville J, J. Math. Pures Appl. 20 (1855), 137-138. [7] Tsarev S P, Tomographical Methods in Physical-Technical Measurements, WNIIFTRI, Moscow, (1985), 120-135. [8] Ferapontov E V, Integration of Weakly Nonlinear Hydrodynamic Systems in Riemann Invariants, Phys. Lett. A158 (1991), 112–118. [9] Adler V E, Marikhin V G and Shabat A B, Lagrangian Lattices and Canonical Bäcklund Transformations, Theor. Math. Phys. 129, Nr. 2 (2001), 163–183..
dspace.entity.typePublication
relation.isAuthorOfPublication896aafc0-9740-4609-bc38-829f249a0d2b
relation.isAuthorOfPublication.latestForDiscovery896aafc0-9740-4609-bc38-829f249a0d2b

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