Skip to main content

One and multidimensional completely integrable systems arising from the isospectral deformation

  • Part IV Two-Dimensional Models and Related Developments
  • Conference paper
  • First Online:
Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 126))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur, Stud. Appl. Math. 53 (1974), pp. 249–315.

    Google Scholar 

  2. N.I. Akhiezer, The classical moment problem, Hafner Publishing Company, 1965. 3. G.G. Appel r ot, Mat. Sbornik v. 16 (1892), Proc. Moscow Univ. Sect. Phys.-Math., No. 11 (1894); N.B. Delone, Algebraic integrals of motion of a rigid body about a fixed point, Petersburg, 1892; V.V. Golubev, Lectures on integration of the equations of motion of a rigid body about a fixed point, Published for NSF, Jerusalem, 1960; D.N. Goryachoff, Math. Sbornic., 21 (1900), No. 3; P. Nekrasov, Math. Sbornik., 16 (1892); V.A. Steklov, Transactions of the physical sciences of the society of amateurs of science, v. 8 (1896).

    Google Scholar 

  3. H.F. Baker, Proc. Royal Soc. London,Ser. A118 (1928), pp. 584–600.

    Google Scholar 

  4. A.A. Belavin, V.E. Zakharov, Pisma JETP 25(1977), No. 12, pp. 603–607.

    Google Scholar 

  5. Yu. M. Berezansky, Trudy Moscow Math. Soc., 21 (1970), pp. 47–102; Yu, M. Berezansky, Self-adjoint eigenfunction expansions, Providence, Rhode Island, 1970.

    Google Scholar 

  6. Yu. M. Berezansky, Self-adjoint operators in spaces of functions with infinite number of variables, Naukova Dumka, Kiev, 1978.

    Google Scholar 

  7. A.S. Budagov, L.A. Takhtajan, Dokl. Acad. Sci., USSR, 235 (1977), No. 4, pp. 805–808.

    Google Scholar 

  8. A.S. Budagov, Proceedings of LOMI, 1970, pp. 24–56.

    Google Scholar 

  9. J.L. Burchnall, T.W. Chaundy, Proc. London Math. Soc., 21 (1922), pp. 420–440

    Google Scholar 

  10. J.L. Burchnall, T.W. Chaundy, Proc. Royal Soc. London, Ser. A118 (1928), 557–573.

    Google Scholar 

  11. F. Calogero, A. Degasperis, Nuovo Cimento 32B (1976), p. 201; F. Calogero, A. Degasperis, Nuovo Cimento 39B (1977), 1.

    Google Scholar 

  12. I.V. Cherednik, Funct. and Appl. 12 (1978), 45.

    Google Scholar 

  13. D.V. Chudnovsky, C.R. Acad. Sci. Paris, A289 (1979), pp. A–429–A–432.

    Google Scholar 

  14. D.V. Chudnovsky, Phys. Lett. A, 74A (1979), pp. 185–188.

    Article  Google Scholar 

  15. D.V. Chudnovsky, Saclay preprint DPh-T/79/80, J. Phys. (to appear).

    Google Scholar 

  16. D.V. Chudnovsky, Lett. Nuovo Cimento, 26 (1979), pp. 423–427.

    Google Scholar 

  17. D.V. Chudnovsky, C.R. Acad. Sci. Paris A289 (1979), pp. A–438–A442.

    Google Scholar 

  18. D.V. Chudnovsky, Riemann monodromy problem, isomonodromy deformation equations and completely integrable systems. Lectures. Cargese Summer School on Mathematical Physics, June 1979, D. Reidel Publishing Company, Dordrecht, Holland (to appear).

    Google Scholar 

  19. D.V. Chudnovsky, The generalized Riemann-Hilbert problem and the spectral interpretation, Proc. Intl. Meeting “Nonlinear evolution equations and dynamical systems”, Lecce, Italy, July 1979, Lect. Notes Physics, Springer-Verlag (to be published).

    Google Scholar 

  20. D.V. Chudnovsky, Saclay preprint DPh-T/79/38, Nuovo Cimento B (to appear).

    Google Scholar 

  21. D.V. Chudnovsky, International Congress of Mathematicians, Helsinki, Finland 1978, Abstract of short communications, p. 183; Notices of the AMS, 26(1979), No. 1, Abstract 763-35-10, p. A-83-A-84.

    Google Scholar 

  22. D.V. Chudnovsky and G.V. Chudnovsky, Nuovo Cimento, 40B (1977), pp. 339–353.

    Google Scholar 

  23. D.V. Chudnovsky and G.V. Chudnovsky, Seminaire sur les equations non-lineaires I (1977–1978), Centre de Mathematiques, Ecole Polytechnique, pp. 300.

    Google Scholar 

  24. D.V. Chudnovsky and G.V. Chudnovsky, Lett. Nuovo Cimento 22 (1978), pp. 31–36; pp. 47–51.

    Google Scholar 

  25. D.V. Chudnovsky and G.V. Chudnovsky, C.R. Acad. Sci. Paris A286 (1978), pp. A–1075–A–1078.

    Google Scholar 

  26. D.V. Chudnovsky and G.V. Chudnovsky, Phys. Lett, A., 72A (1979), pp. 291–293.

    Google Scholar 

  27. D.V. Chudnovsky and G.V. Chudnovsky, Saclay preprint, Dph-T/79/110. 2. Phys. D (to appear).

    Google Scholar 

  28. D.V. Chudnovsky and G.V. Chudnovsky, Seminar on Spectral Theory, Riemann Problem and Complete Integrability, IHES 1979, Paris (to be published); G.V. Chudnovsky, Padé approximation and the Riemann monodromy problem. Lectures. Cargese Summer School on Mathematical Physics, June 1979, D. Reidel Publishing Company, Dordrecht, Holland (to appear).

    Google Scholar 

  29. G. Darboux, C.R. Acad. Sci. Paris, 94 (1882), p. 1456.

    Google Scholar 

  30. P. Deift, E. Trubowitz, Comm. Pure Appl. Math. 32 (1979), 121–200.

    Google Scholar 

  31. A. Degasperis, Lecture Notes in Physics, v. 80, Springer, 1978.

    Google Scholar 

  32. J. Drach, C.R. Acad. Sci. Paris 167 (1918), pp. 743–746; C.R. Acad. Sci: Paris 168(1919), pp. 47–50; pp. 337–340.

    Google Scholar 

  33. B.A. Dubrovin, V.B. Matveev, S.P. Novikov, Russian Math. Survey 31 (1976), 59.

    Google Scholar 

  34. B.A. Dubrovin, Funct. Anal. 11 (1977), No. 4, 28–41.

    Google Scholar 

  35. R. Gamier, Circolo Math. Palermo, 43 (1919), pp. 155–191.

    Google Scholar 

  36. I.M. Gelfand, L.A. Dikij, Funct. Anal. 10 (1976), No. 1, pp. 17–25.

    Google Scholar 

  37. I.M. Gelfand, L.A. Dikij, Russian Math. Survey 20 (1975), No. 5, 77.

    Google Scholar 

  38. I.M. Gelfand, L.A. Dikij, Funct. Anal. Appl. 13 (1979), No. 1, pp. 7–20.

    Google Scholar 

  39. H. Grosse, Institut of Theor. Phys., Univ. Wien, UWThPh-1979-19 (to appear).

    Google Scholar 

  40. J. Honerkamp, Freiburg, 12p. Preprint THEP 79/8, (see this Les Houches volume).

    Google Scholar 

  41. C. Jacobi, Vorlesunger über Dynamic, Berlin, 1843.

    Google Scholar 

  42. D. Kaup, J. Math. Anal. Appl. 59 (1976), 849–864.

    Article  Google Scholar 

  43. W. Koppelman, J. Math. and Mach. (1961), pp. 247–277.

    Google Scholar 

  44. S. Kowalevski, Letters to Mittag-Leffler, Letter from 21 November, 1881. Correspondence, Published by the Academy of Sciences, USSR, 1948; S. Kowalevski, Acta Math., 12(1889), pp. 177–232; Acts. Math. 14(1890).

    Google Scholar 

  45. M.G. Krein, M.A. Krasnoselsky, Uspekhi Math. Nauk 2 (1947), No. 3, 60–106.

    Google Scholar 

  46. J.M. Kritchiver, S.P. Novikov, Funct. Anal. Appl. 12 (1978), pp. 41–52.

    Google Scholar 

  47. P.D. Lax, Commun. Pure Appl. Math. 21 (1968), pp. 467–490; P.D. Lax, Comm. Pure Appl. Math. 28(1975), pp. 141–200.

    Google Scholar 

  48. B.M. Levitan, Math. Sbornik 76 (1968), pp. 239–270.

    Google Scholar 

  49. H.P. McKean, P. van Moerbeke, Invent. Math., 30 (1975), pp. 217–300.

    Article  Google Scholar 

  50. H.P. McKean, E. Trubowitz, Comm. Pure Appl. Math. 29 (1976), pp. 143–226.

    Google Scholar 

  51. O. Neumann, J. Reine Augew. Math. 56 (1859), pp. 46–63.

    Google Scholar 

  52. A.C. Newell, Proc. Royal Soc. London, A365 (1979), pp. 283–311.

    Google Scholar 

  53. L.P. Niznik, Nonstationary inverse scattering problem, Naukova Dumka, Kiev, 1973.

    Google Scholar 

  54. K. Pohlmeyer, K. H. Rehren, Freiburg Preprint 1979, J. Math. Phys. (to appear); Comm. Math. Phys. 46(1976), 207–221; Freiburg Priprint THEP 7916.

    Google Scholar 

  55. L. Schlesinger, J. für Reine Angew. Math. 141 (1912), pp. 96–145.

    Google Scholar 

  56. E.K. Sklvanin, L.A. Takhtadjan, L.D. Fadeev, LOMI preprint P-I-79. Leningrad, 1979, pp. 35.

    Google Scholar 

  57. H.B. Thacker, D.Wilkinson, Fermilab, pub. 79/19-TRY, February 1979 (to appear)

    Google Scholar 

  58. H.B. Thacker, Phys. Rev. D 17 (1978), 1031.

    Article  Google Scholar 

  59. V.E. Zakharov, A.V. Mikhailov, Zr. Eksp. Teor. Fis. 74 (1978), No. 6, pp. 1053–1973.

    Google Scholar 

  60. V.E. Zakharov, A.B. Shabat, Funct. Anal. Appl. 8 (1974), No. 3, pp. 54–56; Funct. Anal. Appl. 13(1979), No. 3, pp. 13–22.

    Google Scholar 

  61. J.L. Gervais, A. Neveu, E.N.S. Preprint (to be published).

    Google Scholar 

  62. E. Borel, Lectures on divergent series, Paris 1928 (English translation ed. by J. Gammel, Los Alamos, LA-6140-TR, 1975).

    Google Scholar 

  63. D.V. Chudnovsky, Proc. Natl. Acad. Sci., USA, 75 (1978), pp. 4082–4084; Lett. Nuovo Cimento 25(1979), pp. 263–265. *** DIRECT SUPPORT *** A3418084 00007

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

D. Iagolnitzer

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Chudnovsky, D.V. (1980). One and multidimensional completely integrable systems arising from the isospectral deformation. In: Iagolnitzer, D. (eds) Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory. Lecture Notes in Physics, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09996-4_49

Download citation

  • DOI: https://doi.org/10.1007/3-540-09996-4_49

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09996-3

  • Online ISBN: 978-3-540-39306-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics