Advertisement

The generalized Riemann-Hilbert problem and the spectral interpretation

  • D. V. Chudnovsky
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 120)

Keywords

Riemann Problem Schrodinger Equation Monodromy Group Linear Differential Operator Nonlinear Schrodinger Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Burchnall, J.L., Chaundy, T.W.: 1922, Proc.London Math.Soc. 21, pp.420–440; 1828, Proc.Soc.London Ser. A118, pp.557–573.Google Scholar
  2. [2]
    Calogero, F., Degasperis, A.: 1976, Nuovo Cimento 32B, p.201; 1977, Nuovo Cimen to 39B, p.l.Google Scholar
  3. [3]
    Degasperis, A.: 1979, Lecture Notes in Physics (to appear).Google Scholar
  4. [4]
    Y.M.Berezansky, Eigenfunction expaasions, AMS, Providence, Rhode Island, 1970.Google Scholar
  5. [5]
    Chudnovsky, D.V.: 1979, Phys.Rev.D (to appear). Service de Physique Théorique, DPh.T. 79/80.Google Scholar
  6. [6]
    Chudnovsky, D.V.: 1979, C.R.Acad.Sci.Paris, (to appear).Google Scholar
  7. [7]
    Chudnovsky, D.V.: 1979, C.R. Acad.Sci.Paris, (to appear).Google Scholar
  8. [8]
    Chudnovsky, D.V. and Chudnovsky, G.V.: (1977–1978) Seminaire sur les équations non-linéaires I, Centre de Mathématiques, Ecole Polytechnique, p.300.Google Scholar
  9. [9]
    Chudnovsky, D.V. and Chudnovsky, G.V.: 1978, Lett.Nuovo Cimento 22, pp.31–36.Google Scholar
  10. [10]
    Chudnovsky, D.V. and Chudnovsky, G.V.: 1978, Lett.Nuovo Cimento 22, pp.47–51.Google Scholar
  11. [11]
    Chudnovsky, D.V. and Chudnovsky, G.V.: 1978, C.R.Acad.Sci.Paris 286A, pp.A1075–A1078.Google Scholar
  12. [12]
    Chudnovsky, D.V. and Chudnovsky, G.V.: 1979, Phys.Lett.72A, pp.291–293 (Utrecht preprint).Google Scholar
  13. [13]
    Chudnovsky, D.V. and Chudnovsky, G.V.: 1979, Phys.Lett.73A, pp.292–294.Google Scholar
  14. [14]
    Chudnovsky, D.V. and Chudnovsky, G.V.: 1979, Seminar on Spectral Theory, Riemann Problem and Complete Integrability IHES, Paris.Google Scholar
  15. [15]
    Drach, J.: 1919, C.R.Acad.Sci.Paris 168, pp.47–50; 1919, C.R.Acad.Sci.Paris 168, pp.337–340.Google Scholar
  16. [16]
    Fuchs, R.: 1905, C.R.Acad.Sci.Paris 141, pp.555–558; 1907, Math.Ann. 63, pp.301–321.Google Scholar
  17. [17]
    Garnier, G., Greene, J.M., Kruskal, M.D., Miura, R.V.: 1974, Comm.Pure Appl.Math. 27, pp.97–120.Google Scholar
  18. [18]
    Garnier, R.: 1919, Circolo Mat. Palermo, 43, pp. 155–191.Google Scholar
  19. [19]
    Gelfand, J.M., Dikij, L.A.: 1975, Russian Math.Survey 30, pp.37–100.Google Scholar
  20. [20]
    Hilbert, D.: Grundzüge der Integralgleichungen, Leipzig-Berlin, 2-te Aufl., 1924.Google Scholar
  21. [21]
    Ince, E.L.: Ordinary differential equations, Dover, 1956.Google Scholar
  22. [22]
    Lappo-Danilevsky, J.A.: Mémoires sur la Theéorie des systémes des Equations Différentielles Linéaires, Chelsea Publishing Company, 1953.Google Scholar
  23. [23]
    Lax, P.: 1968, Comm.Pure Appl.Math. 21, pp.467–490.Google Scholar
  24. [24]
    Painlevé P.: Oeuvres Mathématiques, V 1-3, Paris, 1972.Google Scholar
  25. [25]
    Sato, M., Miwa, T., and Jimbo, M.: 1977, Proc.Japan Acad.53A, pp.6–10, 147–152, 153–158, 183–185, 219–224; 1978 Proc.Japan Acad. 54A, pp.1–5, 36–41, 309–312.Google Scholar
  26. [26]
    Schlesinger, L.: 1912, J. für Reine Angew. M. 141, pp.96–145.Google Scholar
  27. [27]
    Kaup, D.: 1976, J.Math.Analy.Appl. 54, p.l.Google Scholar
  28. [28]
    Zakharov, V.E., Mikhailov, A.V.: 1978, JETP 74, pp.1953–1970.Google Scholar
  29. [29]
    Zakharov, V.Z., Shabat, A.B.: 1974, Funct.Anal.Appl. 8, pp.43–57.Google Scholar
  30. [30]
    Riemann, B.: Oeuvres Mathdmathiques, Albert Blanchard, Paris, 1968, pp.353-363.Google Scholar
  31. [31]
    Krein, M.G., Daleekij, Y.L.: Stability of solutions linear differential equations in the Hilbert space, AMS, Providence, 1972.Google Scholar
  32. [32]
    Krein, S.G.: Differential equations in Banach spaces, AMS, Providence, 1971.Google Scholar
  33. [33]
    Thacker, H.B., Wilkinson, D.: 1979, Fermilab-Pub-79, 19-THY.Google Scholar
  34. [34]
    Honerkamp: 1979, Freiburg Preprint.Google Scholar
  35. [35]
    Ablowitz, M.J., Kaup, D.J., Newell, A.C. and Segur, H.: 1974, J.Math.Phys. 15, p.1852.Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • D. V. Chudnovsky
    • 1
  1. 1.D.Ph.T.CEN-Saclay-91190Gif-sur-YvetteFrance

Personalised recommendations