Theoretical and Mathematical Physics

, Volume 122, Issue 1, pp 29–38 | Cite as

A new construction of recursion operators for systems of the hydrodynamic type

  • A. P. Fordy
  • T. B. Gürel

Abstract

We consider a certain class of two-dimensional systems of the hydrodynamic type that contains all examples known to us and can be associated with a class of linear wave equations possessing an algebra of ladder operators. We use this to give a simple construction of recursion operators for these systems, not always coinciding with those of Sheftel and Teshukov.

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References

  1. 1.
    B. A. Dubrovin and S. P. Novikov,Sov. Math. Dokl.,27, 665–669 (1983).Google Scholar
  2. 2.
    S. P. Tsarev,Math. USSR Izv.,37, 397–419 (1991).CrossRefMathSciNetGoogle Scholar
  3. 3.
    M. B. Sheftel,Theor. Math. Phys.,56, 878–891 (1983).CrossRefMathSciNetGoogle Scholar
  4. 4.
    V. M. Teshukov, “Hyperbolic systems admitting a nontrivial Lie-Bäcklund group,” Preprint No. 106, LHAN, Leningrad (1989) [in Russian].Google Scholar
  5. 5.
    M. B. Sheftel, “Generalized hydrodynamic-type systems,” in:CRC Handbook of Lie Group Analysis of Differential Equations (N. H. Ibragimov, ed.) (Vol. 3, No. 7), CRC Press, New York (1996), pp. 169–189.Google Scholar
  6. 6.
    E. G. Kalnins, S. Benenti, and W. Miller, Jr.,J. Math. Phys.,38, 2345–2365 (1997)CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    E. T. Copson,Partial Differential Equations, Cambridge Univ. Press, Cambridge (1975).MATHGoogle Scholar
  8. 8.
    P. J. Olver,Application of Lie Groups to Differential Equations, Springer, New York (1986).Google Scholar
  9. 9.
    E. V. Ferapontov, “Hydrodynamic-type systems,” in:CRC Handbook of Lie Group Analysis of Differential Equations (N. H. Ibragimov, ed.) (Vol. 1, No. 14), CRC Press, New York (1994), pp. 303–331.Google Scholar
  10. 10.
    E. V. Ferapontov and A. P. Fordy,J. Geom. Phys.,21, 169–182 (1997).CrossRefMathSciNetGoogle Scholar
  11. 11.
    E. V. Ferapontov and M. V. Pavlov,Physica D,52, 211–219 (1991).CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    D. Fairlie and I. A. B. Strachan,Physica D,90, 1–8 (1996).CrossRefMathSciNetGoogle Scholar
  13. 13.
    J. Gibbons and S. P. Tsarev,Phys. Lett. A,211, 19–24 (1996).CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • A. P. Fordy
    • 1
  • T. B. Gürel
    • 2
    • 3
  1. 1.Department of Applied Mathematics and Centre for Nonlinear StudiesUniversity of LeedsUK
  2. 2.Department of Applied Mathematics and Centre for Nonlinear StudiesUniversity of LeedsUK
  3. 3.Department of MathematicsBilkent UniversityAnkaraTurkey

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