Conservation of Hamiltonian structures in Whitham's averaging method

Izvestiya Mathematics

Volumn 63, Issue 6, 1999, Pages 1171-1201

  Maltsev, A Ya ^a  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12844252460     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM1999v063n06ABEH000269     Document Type: Article

References (26)

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3. B. A. Dubrovin and S. P. Novikov, "Hamiltonian formalism for one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method", Dokl. Akad. Nauk SSSR 270 (1983), 781-785;
4. English transl., Soviet Math. Dokl. 27 (1983), 665-669.
5. B. A. Dubrovin and S. P. Novikov, "Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory", Uspekhi Mat. Nauk 44:6 (1989), 29-98;
6. English transl., Russian Math. Surveys 44:6 (1989), 35-124.
7. S. Yu. Dobrokhotov and V. P. Maslov, "Finite-gap almost periodic solutions in the WKB-approximation", Itogi Nauki i Tekhniki. Sovrem. Probl. Mat., vol. 15, VINITI, Moscow 1980. (Russian)
8. I. M. Krichever, "The averaging method for two-dimensional "integrable" equations", Funktsional Anal. i Prilozhen. 22:3 (1988), 37-52;
9. English transl., Functional Anal. Appl. 22 (1988), 200-213.
10. I. M. Krichever, "Spectral theory of two-dimensional periodic operators and its applications", Uspekhi Mat. Nauk 44:2 (1989), 121-184;
11. English transl., Russian Math. Surveys 44:2 (1989), 145-225.
12. I. M. Krichever, "Perturbation theory in periodic problems for two-dimensional integrable systems", Sov. Sci. Rev. Section C 9 (1992).
13. S. P. Tsarev, "On Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type", Dokl. Akad. Nauk SSSR 282 (1985), 534-537;
14. English transl., Soviet Math. Dokl. 31 (1985), 488-491.
15. j which do not possess Riemann invariants", Physica D 63 (1993), 50-70.
16. E. V. Ferapontov, "On the matrix Hopf equation and integrable Hamiltonian systems of hydrodynamic type which do not possess Riemann invariants", Physics Letters A 179 (1993), 391-397.
17. S. P. Novikov and A. Ya. Maltsev, "The Liouville form of averaged Poisson brackets", Uspekhi Mat. Nauk 48:1 (1993), 155-156;
18. English transl., Russian Math. Surveys 48:1 (1993), 155-157.
19. O. I. Mokhov, "Local third-order Poisson brackets", Uspekhi Mat. Nauk 40:5 (1985), 257-258;
20. English transl., Russian Math. Surveys 40:5 (1985), 233-234.
21. O. I. Mokhov, "Hamiltonian differential operators and contact geometry", Funktsional. Anal. i Prilozhen. 21:3 (1987), 53-60;
22. English transl., Functional Anal. Appl. 21 (1987), 217-223.
23. N. I. Grinberg, "On Poisson brackets of hydrodynamic type with degenerate metric", Uspekhi Mat. Nauk 40:4 (1985), 217-218;
24. English transl, in Russian Math. Surveys 40:4 (1985).
25. A. Ya. Maltsev and M. V. Pavlov, "On Whitham's averaging method", Funktsional. Anal. i Prilozhen. 29:1 (1995), 7-24;
26. English transl., Functional Anal. Appl. 29 (1995), 6-19.