A new construction of recursion operators for systems of the hydrodynamic type
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 37-49 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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A. P. Fordy; T. B. Gürel. A new construction of recursion operators for systems of the hydrodynamic type. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 37-49. http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a3/

[1] B. A. Dubrovin, S. P. Novikov, DAN SSSR, 270 (1983), 781–785 | MR | Zbl

[2] S. P. Tsarev, Izv. AN SSSR. Ser. matem., 54:2 (1990), 1048–1068 | MR | Zbl

[3] M. B. Sheftel, TMF, 56 (1983), 387–394 | MR

[4] V. M. Teshukov, Giperbolicheskie sistemy, dopuskayuschie netrivialnuyu gruppu Li–Beklunda, Preprint No 106, LIIAN, L., 1989

[5] M. B. Sheftel, “Generalised hydrodynamic-type systems”, CRC Handbook of Lie Group Analysis of Differential Equations, 3, no. 7, ed. N. H. Ibragimov, CRC Press, New York, 1996, 169–189 | MR

[6] E. G. Kalnins, S. Benenti, W. Miller, Jr., J. Math. Phys., 38 (1997), 2345–2365 | DOI | MR | Zbl

[7] E. T. Copson, Partial Differential Equations, Cambridge Univ. Press, Cambridge, 1975 | MR | Zbl

[8] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | Zbl

[9] E. V. Ferapontov, “Hydrodynamic-type systems”, CRC Handbook of Lie Group Analysis of Differential Equations, 1, no. 14, ed. N. H. Ibragimov, CRC Press, New York, 1994, 303–331 | MR

[10] E. V. Ferapontov, A. P. Fordy, J. Geom. Phys., 21 (1997), 169–182 | DOI | MR | Zbl

[11] E. V. Ferapontov, M. V. Pavlov, Physica D, 52 (1991), 211–219 | DOI | MR | Zbl

[12] D. Fairlie, I. A. B. Strachan, Physica D, 90 (1996), 1–8 | DOI | MR | Zbl

[13] J. Gibbons, S. P. Tsarev, Phys. Lett. A, 211 (1996), 19–24 | DOI | MR | Zbl