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On the construction of evolution equations admitting a master symmetry

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dc.contributor.authorFinkel Morgenstern, Federico
dc.contributor.authorFokas, A. S.
dc.date.accessioned2023-06-20T20:08:44Z
dc.date.available2023-06-20T20:08:44Z
dc.date.issued2002-01-21
dc.description©2002 Elsevier Science B.V. All rights reserved. F.F. would like to express his gratitude to the Department of Mathematics of Imperial College for its hospitality. A.S.F. is grateful to J. Sanders for useful suggestions. This work was partially supported by EPSRC grant No. GR/M61450 and by DGES grant PB98-0821.
dc.description.abstractA method for constructing evolution equations admitting a master symmetry is proposed. Several examples illustrating the method are presented. It is also noted that for certain evolution equations master symmetries can be useful for obtaining new conservation laws from a given one.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipEPSRC
dc.description.sponsorshipDGES
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/31404
dc.identifier.doi10.1016/S0375-9601(01)00836-2
dc.identifier.issn0375-9601
dc.identifier.officialurlhttp://dx.doi.org/10.1016/S0375-9601(01)00836-2
dc.identifier.relatedurlhttp://www.sciencedirect.com
dc.identifier.relatedurlhttp://arxiv.org/abs/nlin/0112002
dc.identifier.urihttps://hdl.handle.net/20.500.14352/59669
dc.issue.number4-feb.
dc.journal.titlePhysics letters A
dc.language.isoeng
dc.page.final44
dc.page.initial36
dc.publisherElsevier
dc.relation.projectIDGR/M61450
dc.relation.projectIDPB98-0821
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordMaster symmetries
dc.subject.keywordIntegrable evolution equations
dc.subject.keywordConservation laws
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleOn the construction of evolution equations admitting a master symmetry
dc.typejournal article
dc.volume.number293
dcterms.references[1] A. S. Fokas and B. Fuchssteiner, The hierarchy of the Benjamin–Ono equation, Phys. Lett. 86A (1981) 341–5. [2] H. H. Chen, Y. C. Lee and J.-E. Lin, On a new hierarchy of symmetries for the Benjamin–Ono equation, Phys. Lett. 91A (1982) 381–3. [3] H. H. Chen, Y. C. Lee and J.-E. Lin, On a new hierarchy of symmetries for the Kadomtsev– Petviashvili equation, Physica 9D (1983) 439–45. [4] B. Fuchssteiner, Mastersymmetries, higher order time-dependent symmetries and conserved densities of nonlinear evolution equations, Prog. Theoret. Phys. 70 (1983) 1508–22. [5] A. S. Fokas, Symmetries and integrability, Stud. Appl. Math. 77 (1987) 253–99. [6] I. Y. Dorfman, Dirac structures and integrability of nonlinear evolution equations, Nonlinear Science: Theory and Applications, John Wiley & Sons, Ltd., Chichester, 1993. [7] J. P. Zubelli and F. Magri, Differential equations in the spectral parameter, Darboux transformations and a hierarchy of master symmetries for KdV, Commun. Math. Phys. 141 (1991) 329–51. [8] F. A. Grünbaum and L. Haine, A theorem of Bochner, revisited, in Algebraic aspects of ntegrable systems, A. S. Fokas and I. M. Gel’fand (Eds.), Birkh¨auser, Boston, 1997. [9] A. V. Mikhailov and V. V. Sokolov, Integrable ODEs on associative algebras, Commun. Math. Phys. 211 (2000) 231–51. [10] A. S. Fokas, A symmetry approach to exactly-solvable evolution equations, J. Math. Phys. 21 (1980) 1318–25. [11] J. A. Sanders and J. P. Wang, On the integrability of homogeneous scalar evolution equations, J. Differential Equations 147 (1998) 410–34. [12] N. K. Ibragimov and A. B. Shabat, Infinite Lie–Bäcklund algebras, Funct. Anal. Appl. 14 (1981) 313–5. [13] F. Calogero, The evolution PDE ut = uxxx + 3(uxxu 2 + 3u 2 xu) + 3uxu 4 , J. Math. Phys. 28 (1987) 538–55. [14] P. J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, Berlin, 1993. [15] A. V. Mikhailov, A. B. Shabat and V. V. Sokolov, The symmetry approach to classification of integrable equations, in What is Integrability, V.E. Zakharov (Ed.), Springer-Verlag, Berlin, 1991. [16] W. Oevel and B. Fuchssteiner, Explicit formulas for symmetries and conservation laws for the Kadomtsev–Petviashvili equation, Phys. Lett. 88A (1982) 323–7. [17] K. Sawada and T. Kotera, A method for finding N-soliton solutions of the K.d.V. equation and K.d.V-like equation, Prog. Theoret. Phys. 51 (1974) 1355–67. [18] B. Fuchssteiner and W. Oevel, The bi-Hamiltonian structure of some nonlinear fifth- and seventh-order differential equations and recursion formulas for their symmetries and conserved covariants, J. Math. Phys. 23 (1982) 358–63. [19] B. Fuchssteiner, Application of hereditary symmetries to nonlinear evolution equations, Nonlinear Anal. Theory Meth. Appl. 3 (1979) 849–62.
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