Pole interpretation of one-dimensional completely integrable systems of Korteweg-de Vries and Burgers-Hopf type

D. V. Choodnovsky

Séminaire sur les équations non linéaires (Choodnovsky) (1977-1978)

  • page 1-25

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Choodnovsky, D. V.. "Pole interpretation of one-dimensional completely integrable systems of Korteweg-de Vries and Burgers-Hopf type." Séminaire sur les équations non linéaires (Choodnovsky) (1977-1978): 1-25. <http://eudml.org/doc/112148>.

@article{Choodnovsky1977-1978,
author = {Choodnovsky, D. V.},
journal = {Séminaire sur les équations non linéaires (Choodnovsky)},
language = {eng},
pages = {1-25},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Pole interpretation of one-dimensional completely integrable systems of Korteweg-de Vries and Burgers-Hopf type},
url = {http://eudml.org/doc/112148},
year = {1977-1978},
}

TY - JOUR
AU - Choodnovsky, D. V.
TI - Pole interpretation of one-dimensional completely integrable systems of Korteweg-de Vries and Burgers-Hopf type
JO - Séminaire sur les équations non linéaires (Choodnovsky)
PY - 1977-1978
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 25
LA - eng
UR - http://eudml.org/doc/112148
ER -

References

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  1. 1 D.V. Choodnovsky, G.V. Choodnovsky, Nuov. Cim.40B No 2 (1977) 339-353. 
  2. 2 M.A. Olshanetzky and A.M. Perelomov, Inv. Math.37 (1976). See also M.A. Olshanetzky and A.M. Perelomov, Lett. Math. Phys.1 (1976) 187; Lett. Nuov. Cim.16 (1976) 333; 17 (1976) 97. 
  3. 3 J. Moser, Adv. Math.16 (1975) 197. See also the article by J. Moser: in the Battelle Seattle 1974 Rencontres Proceeedings (J. Moser, Editor: Theory and applications in Lect. Notes in Physics, vol. 38, Berlin1975). 
  4. 4 F. Calogero, C. Marchioro and O. Ragnisco, Lett. Nuov. Cim.13 (1975) 383. MR443665
  5. 5 F. Calogero, Lett.Nuov. Cim.13 (1975) 411. MR388895
  6. 6 W.R. Thikstun, J. Math. Anal. Appl.55 (1976) 335. MR424060
  7. 7 M.D. Kruskal, Lectures in Appl.Math. Amer. Math. Soc.15 (1974) 61. MR352741
  8. 8 H. Airault, H.P. McKean and J. Moser, Comm. Pure Appl. Math.55 (1977). MR649926
  9. 9 F. Calogero, Lett.Nuov. Cim.16 (1976) 77. MR446155
  10. 10 B. Sutherland, Phys. Rev.A5 (1972) 1372. 
  11. 11 F. Calogero, Lett.Nuov. Cim.13 (1975) 507. MR388895
  12. 12 A. Erdelyi, Editor: Higher transcendental functions, vol. 2 (New York, N.Y.1953). Zbl0051.30303
  13. 13 M. Kac and P. van Moerbecke, Proc. Nat. Acad. Sci.72 (1975) 1627. Zbl0343.34003MR367360
  14. 14 J. Ford, in Lectures in Statitical Physics, Lecture Notes in Physics, vol. 28 (Berlin, 1974) p. 204. 
  15. 15 I.M. Krichever, Uspechi Math. Nauk v. 33 No 5 (1977) (Russian). 
  16. 16 F. Calogero, Lett.Nuov. Cim.16 (1976) 35. MR446154
  17. 17 J. Cole, Quart. Appl. Math.9 (1951) 225. Zbl0043.09902MR42889
  18. 18 R. Hirota, Direct method of finding exact solutions of nonlinear evolution equations, in "Bäcklund Transformations", edited by R. Miura, Lecture Notes in Maths. Vol. 515 (Berlin1976) 61. Zbl0336.35024MR609746
  19. 19 Exact treatment of non-linear lattice waves, Suppl. Prog. Theor. Phys.59 (1976) (see p. 97). 
  20. 20 B.A. Dubrovin, V.B. Matveev and S.P. Novikov, Usp. Math. Nauk31 (1976) 55 (Russian). MR427869
  21. 21 D.V. Choodnovsky, G.V. Choodnovsky, Preprint, Kiev1976 (unpublished) 
  22. 22 D.V. Choodnovsky, G.V. Choodnovsky, Lett. Nuov. Cim.19 No 8 (1977). 
  23. 23 J.L. Burchnall, T.W. Chaundy, Proc. London Math. Soc.21 (1922) 420-440. JFM49.0311.03
  24. 24 P. Lax, Comm. Pure Appl. Math.21 No 5 (1968) 467-490. Zbl0162.41103MR235310
  25. 25 J.L. Burchnall, T.W. Chaundy, Proc. Royal Soc. London, Ser. A118 (1928) 557-573. JFM54.0439.01
  26. 26 H. Airault, J. Moser, Preprint. 
  27. 28 S.V. Manakov, V.E. Zakhanov, L. Bordag, A. Its, V. Matveev, Phys. Letters, 63A No 3 (1977). 
  28. 29 M. Adler, J. Moser, Preprint (to be published). 
  29. 31 F. Calogero, Nuov. Cim. (1978). 

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