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Journal of Mathematical Physics / Volume 29 / Issue 1

J. Math. Phys. 29, 1 (1988); http://dx.doi.org/10.1063/1.528173 (8 pages)

On the infinite‐dimensional symmetry group of the Davey–Stewartson equations

B. Champagne and P. Winternitz

Centre de recherches mathématiques, Université de Montréal, C.P. 6128, Succ. A, Montréal, Québec, Canada, H3C 3J7

(Received 19 February 1987; accepted 5 August 1987)

The Lie algebra of the group of point transformations, leaving the Davey–Stewartson equations (DSE’s) invariant, is obtained. The general element of this algebra depends on four arbitrary functions of time. The algebra is shown to have a loop structure, a property shared by the symmetry algebras of all known (2+1)‐dimensional integrable nonlinear equations. Subalgebras of the symmetry algebra are classified and used to reduce the DSE’s to various equations involving only two independent variables.

KEYWORDS and PACS

Keywords

SYMMETRY GROUPS, DIMENSIONS, LIE GROUPS, ALGEBRA, INVARIANCE PRINCIPLES, TRANSFORMATIONS, INTEGRABLE SYSTEMS, TIME DEPENDENCE, WAVE EQUATIONS, DIFFERENTIAL EQUATIONS

PACS

  • 02.20.Bb

    General structures of groups

  • 41.20.Jb

    Electromagnetic wave propagation; radiowave propagation

  • 45.05.+x

    General theory of classical mechanics of discrete systems

  • 02.20.Qs

    General properties, structure, and representation of Lie groups

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.528173

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    D. David, N. Kamran, D. Levi, and P. Winternitz, Phys. Rev. Lett. 55, 2111 (1985)
    J. Math. Phys. 27, 1225 (1986JMAPAQ000027000005001225000001).

    B. Dorizzi, B. Grammaticos, A. Ramani, and P. Winternitz, J. Math. Phys. 27, 2848 (1986JMAPAQ000027000012002848000001).

    R. A. Leo, L. Martina, and G. Soliani, J. Math. Phys. 27, 2623 (1986JMAPAQ000027000011002623000001).

    J. Patera, P. Winternitz, and H. Zassenhaus, J. Math. Phys. 16, 1597, 1615 (1975JMAPAQ000016000008001597000001).

    J. Patera, R. T. Sharp, P. Winternitz, and H. Zassenhaus, J. Math. Phys. 18, 2259 (1977JMAPAQ000018000012002259000001).



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