Generalized hodograph method from the group-theoretical point of view
Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 2, pp. 205-210 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the scale invariance of equations of hydrodynamic type leads to an algebraic construction of a series of group-invariant solutions corresponding to the generalized hodograph method. A solution of Whitham's equations for the KdV equation is obtained for certain initial conditions.
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V. R. Kudashev; S. E. Sharapov. Generalized hodograph method from the group-theoretical point of view. Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 2, pp. 205-210. http://geodesic.mathdoc.fr/item/TMF_1990_85_2_a4/

[1] Dubrovin B. A., Novikov S. P., UMN, 44:6 (1989), 29–98 | MR | Zbl

[2] Tsarev S. P., DAN SSSR, 282:3 (1985), 534–537 | MR | Zbl

[3] Krichever I. M., Funkts. analiz i ego prilozh., 22:3 (1988), 37–52 | MR | Zbl

[4] Kodama Y., Phys. Lett. A, 135A:3 (1989), 171–174 | DOI | MR

[5] Kodama Y., Nonlinear World Proceedings of the IV International Workshop on Nonlinear and Turbulent Processes in Physics, V. 2, Naukova dumka, Kiev, 1989, 115–118

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

[7] Gurevich A. V., Krylov A. L., Mazur N. G., ZhETF, 95:5 (1989), 1674–1689

[8] Pavlov M. V., TMF, 73:2 (1987), 316–320 | MR

[9] Meshkov A. G., Mikhalyaev B. B., TMF, 72:2 (1987), 163–171 | MR | Zbl

[10] Nyuell A., Solitony v matematike i fizike, Mir, M., 1989 | MR

[11] Whitham G. B., Proc. Roy. Soc., A283 (1965), 238–261 | DOI | MR | Zbl