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Solitons. Theory and application

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La Rivista del Nuovo Cimento (1971-1977)

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References

  1. E. Fermi, J. R. Pasta andS. M. Ulam: Los Alamos Sci. Lab. Rep. LA-1940 (1955).

  2. N. J. Zabusky: inNonlinear Partial Differential Equations, edited byW. Ames (New York, N. Y., 1967), p. 223.

  3. D. J. Korteweg andG. de Vries:Phil. Mag.,39, 422 (1895).

    Article  MATH  Google Scholar 

  4. J. Scott-Russell:Proc. Roy. Soc. Edinburgh, 319 (1844).

  5. N. J. Zabusky amdM. D. Kruskal:Phys. Rev. Lett.,15, 240 (1965).

    Article  ADS  MATH  Google Scholar 

  6. J. K. Perring andT. H. R. Skyrme:Nucl. Phys.,31, 550 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Seeger, H. Donth andA. Kochendörfer:Zeits. Phys.,31, 550 (1962).

    Google Scholar 

  8. L. van Vijngarden:Journ. Fluid Mech.,33, 465 (1968).

    Article  ADS  Google Scholar 

  9. S. Leibovich:Journ. Fluid Mech.,42, 803 (1970).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. J. Frenkel andT. Kontorova:Journ. Phys. USSR,1, 137 (1939).

    MathSciNet  MATH  Google Scholar 

  11. C. P. Beam andR. W. de Blois:Bull. Amer. Phys. Soc.,4, 53 (1959).

    Google Scholar 

  12. V. Enz:Helv. Phys. Acta,37, 245 (1964).

    Google Scholar 

  13. I. O. Kulik:Sov. Phys. JETP,24, 1307 (1967).

    ADS  Google Scholar 

  14. P. Lebwohl andM. J. Stephen:Phys. Rev.,163, 376 (1967).

    Article  ADS  Google Scholar 

  15. A. C. Scott:Bull. Amer. Phys. Soc.,12, 308 (1967).

    Google Scholar 

  16. A. C. Scott andW. J. Johnson:Appl. Phys. Lett.,14, 316 (1969).

    Article  ADS  Google Scholar 

  17. A. C. Scott:Nuovo Cimento,69 B, 241 (1970).

    Article  ADS  Google Scholar 

  18. V. I. Bespalov andV. I. Talanov:JEPT Lett.,3, 307 (1966).

    ADS  Google Scholar 

  19. P. L. Kelley:Phys. Rev. Lett.,15, 1005 (1965).

    Article  ADS  Google Scholar 

  20. V. I. Talanov:JEPT Lett.,2, 138 (1965).

    ADS  Google Scholar 

  21. A. Hasegawa andF. Tappert:Appl. Phys. Lett.,23, 142 (1973).

    Article  ADS  Google Scholar 

  22. V. I. Karpman andE. M. Kruskal:Sov. Phys. JETP,28, 277 (1969).

    ADS  Google Scholar 

  23. F. Tappert andC. M. Varma:Phys. Rev. Lett.,25, 1108 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  24. T. Tanuiti andH. Washimi:Phys. Rev. Lett.,21, 209 (1968).

    Article  ADS  Google Scholar 

  25. B. D. Fried andY. H. Ychikawa:Journ. Phys. Soc. Japan,34, 1073 (1973).

    Article  ADS  Google Scholar 

  26. I. H. Ychikawa, T. Imamura andT. Tanuiti:Journ. Phys. Soc. Japan,33, 189 (1972).

    Article  ADS  Google Scholar 

  27. K. Shimizu andY. H. Ychikawa:Journ. Phys. Soc. Japan,33, 789 (1972).

    Article  ADS  Google Scholar 

  28. C. S. Gardner, J. M. Greene, M. D. Kruskal andR. M. Miura:Phys. Rev. Lett.,19, 1095 (1967).

    Article  ADS  Google Scholar 

  29. P. D. Lax:Comm. Pure Appl. Math.,21, 467 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  30. I. M. Gelfand andB. M. Levitan:Amer. Math. Soc. Transl.,1, 253 (1955).

    MathSciNet  Google Scholar 

  31. V. de Alfaro andT. Regge:Potential Scattering (Amsterdam, 1965).

  32. R. Hirota:Phys. Rev. Lett.,27, 1192 (1971).

    Article  ADS  MATH  Google Scholar 

  33. A. C. Scott, F. V. F. Chu andD. W. McLaughlin:Proc. IEEE,61, 1443 (1973).

    Article  MathSciNet  ADS  Google Scholar 

  34. V. E. Zakharov andL. D. Faddeev:Funct. Anal. Appl.,5, 280 (1971).

    Article  Google Scholar 

  35. O. Bäcklund:Lunds Universitets Arsskrift,19, 1 (1883).

    Google Scholar 

  36. L. Eisenhart:A Treatise on the Differential Geometry of Curves and Surfaces (New York, N. Y., 1960).

  37. L. Bianchi:Lezioni di geometria differenziale, Vol.2 (Pisa, 1902).

  38. P. J. Caudrey, J. D. Gibbon, J. C. Eilbeck andR. K. Bullough:Phys. Rev. Lett.,30, 237 (1973).

    Article  ADS  Google Scholar 

  39. M. J. Ablowitz, D. J. Kaup, A. C. Newell andH. Segur:Stud. Appl. Math.,53, 249 (1974).

    MathSciNet  MATH  Google Scholar 

  40. R. Hirota:Journ. Math. Phys.,14, 805 (1973).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  41. M. J. Ablowitz, D. J. Kaup, A. C. Newell andH. Segur:Phys. Rev. Lett.,31, 125 (1973).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. H. D. Wahlquist andF. B. Estabrook:Phys. Rev. Lett.,31, 1386 (1973).

    Article  MathSciNet  ADS  Google Scholar 

  43. G. L. Lamb jr.:Journ. Math. Phys.,12, 2157 (1974).

    Article  MathSciNet  ADS  Google Scholar 

  44. V. E. Zakharov andA. B. Shabat:Sov. Phys. JETP,34, 62 (1972).

    MathSciNet  ADS  Google Scholar 

  45. A. G. Lindgren andR. J. Buratti:IEEE Trans. Circuit Theory, CT-16, 274 (1969).

    Article  Google Scholar 

  46. A. Jeffrey andT. Kakutami:Ind. Univ. Math. Journ.,20, 463 (1970).

    Article  MATH  Google Scholar 

  47. A. J. Callegari andE. L. Reiss:Journ. Math. Phys.,14, 267 (1973).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. T. B. Benjamin:Proc. Roy. Soc.,328 A, 153 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  49. M. Kako andG. Rowlands:Plasma Phys.,18, 165 (1975).

    Article  ADS  Google Scholar 

  50. A. N. Kolmogorov:Proceedings of the 1954International Congress on Mathematics (Amsterdam, 1957), p. 315.

  51. J. Zabuski:Comp. Phys. Comm.,5, 1 (1973).

    Article  ADS  Google Scholar 

  52. V. Narayamurti andC. M. Varma:Phys. Rev. Lett.,25, 1105 (1970).

    Article  ADS  Google Scholar 

  53. R. E. Pejerls: inTheoretical Physics in the Twentieth Century (Pauli Memorial Volume), edited byM. Fierz andV. Weisskopf (New York, N. Y., 1960), p. 140.

  54. D. N. Payton III,M. Rich andW. M. Visscher:Phys. Rev.,160, 706 (1967).

    Article  ADS  Google Scholar 

  55. M. Rich, W. M. Visscher andD. N. Payton III:Phys. Rev. A,4, 1682 (1971).

    Article  ADS  Google Scholar 

  56. G. B. Whitham:Journ. Fluid Mech.,22, 273 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  57. G. B. Whitham:Proc. Roy. Soc.,283 A, 238 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  58. G. B. Whitham:Journ. Fluid Mech.,27, 399 (1967).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  59. G. B. Whitham:Proc. Roy. Soc.,299 A, 6 (1967).

    Article  ADS  Google Scholar 

  60. W. J. Johnson: Ph. D. Thesis, University of Wisconsin (1968).

  61. H. Washimi andT. Tanuiti:Phys. Rev. Lett.,17, 996 (1968).

    Article  ADS  Google Scholar 

  62. A. Barone, F. Esposito, C. J. Magee andA. C. Scott:Riv. Nuovo Cimento,1, 227 (1971).

    Article  Google Scholar 

  63. S. I. Ben Abraham:Phys. Lett.,55 A, 383 (1976).

    Article  ADS  Google Scholar 

  64. A. M. Ablowitz andR. Haberman:Phys. Rev. Lett.,35, 1185 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  65. A. C. Scott:A classical model for boson condensation, preprint (1975).

  66. R. Rajaraman:Some nonperturbative semi-classical methods in quantum field theory, AEC 2220-47 (May 1975).

  67. S. Kumei:Journ. Math. Phys.,16, 2461 (1975).

    Article  MathSciNet  ADS  Google Scholar 

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Paper based on a series of lectures given at the National Colloquium on « Interdisciplinary Aspects of Modern Physics » organized by the Post-Graduate School on Solid State Physics of the Parma University in May 1976.

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Cercignani, C. Solitons. Theory and application. Riv. Nuovo Cim. 7, 429–469 (1977). https://doi.org/10.1007/BF02747772

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