Plasma Physics pp 456-474 | Cite as

Self-Similar Solutions of Nonlinear Evolution Equations of Physical Significance

  • R. Nakach
Part of the Nobel Symposium Committee (1976) book series (NOFS, volume 36)


One of the most remarkable recent advances in mathematical physics is a method of solution for certain classes of nonlinear partial differential equations which arise naturally in many scientific areas, and particularly in nonlinear plasma physics.


Nonlinear Evolution Equation Resonant Interaction mKdV Equation Inverse Scattering Problem Nonlinear Schrodinger Equation 
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  1. 1.
    Gardner, C.S., J.M. Greene, M.D. Kruskal, R.M. Miura, Phys. Rev, Letters, 19, 1095, (1967).ADSCrossRefGoogle Scholar
  2. 2.
    Lax, P.D., Comm. on Pure and Appl. Math., 21, 467, (1968).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Zakharov, V.E., A.B. Shabat, Zh. Eksp. Teor. Fiz., 61, 118 (1971)Google Scholar
  4. Zakharov, V.E., A.B. Shabat, Soy. Phys. JETP, 34, 62, (1972)MathSciNetADSGoogle Scholar
  5. 4.
    Zakharov, V.E., A.B. Shabat, Zh, Eksp. Teor. Fiz., 64, 1627, (1971)Google Scholar
  6. Zakharov, V.E., A.B. Shabat, Soy. Phys. JETP, 37, 823, (1973)ADSGoogle Scholar
  7. 5.
    Zakharov, V.E., Zh. Eksp. Teor, Fiz., 65, 219 (1973)Google Scholar
  8. Zakharov, V.E., Soy. Phys. JETP, 38, 108, (1974).ADSGoogle Scholar
  9. 6.
    Fermi, E., J. Pasta, S. Ulam, Los Alamos Scientific Report LA-1940, (1955).Google Scholar
  10. 7.
    Zakharov, V.E., S.U. Manakov, Zh. Eksp. Teor, Fiz. Pis’ma Red., 18, 413, (1973)ADSGoogle Scholar
  11. Zakharov, V.E., S.U. Manakov, JETP Lett., 18, 243, (1973)ADSGoogle Scholar
  12. 8.
    Ablowitz, M.J., D.J. Kaup, A.C. Newell, H. Segur, Phys. Rev. Letters, 30, 1262, (1973).MathSciNetADSCrossRefGoogle Scholar
  13. 9.
    Ince, E.L., Ordinary Differential Equations, p. 315, (Dover 1956 ).Google Scholar
  14. 10.
    Idura, R.M, Journal of Math. Phis, 9, 1202, (1968).ADSCrossRefGoogle Scholar
  15. 11.
    Ablowitz, M.J., D.J. Kaup, A.C. Newell, H. Segur, Phys. Rev. Letters, 31, 125, (1973).MathSciNetADSCrossRefMATHGoogle Scholar
  16. 12.
    Kato, Y., Suppl. of the Progress of Theor. Physics, 55, 247, (1974).ADSCrossRefGoogle Scholar
  17. 13.
    Kodama, Y., Progress of Theor. Physics., 5b, 669, (1975).MathSciNetADSCrossRefGoogle Scholar
  18. 14.
    Nakach, R.D., Report EUR-CEA-FC 803, (1975).Google Scholar
  19. 15.
    Kadomtsev, B.B., V.I. Karpman, Soy. Phys. USPEKHI, 14, 40, (1971).MathSciNetADSCrossRefGoogle Scholar
  20. 16.
    Bespalov, V.I., A.G. Litvak, V.I. Talanov, (Second A11-union Symp. on Nonlinear Optics), 1966, collection of papers, NAUKA, 1968.Google Scholar
  21. 17.
    Karpman, V.I., E.M. Krushkal, Zh. Eksp. Teor. Fiz., 55, 530, (1968)Google Scholar
  22. Karpman, V.I., E.M. Krushkal, Sov. Phys. JETP, 28, 277, (1969).ADSGoogle Scholar
  23. 18.
    Lamb, Jr., G.L., Review of Modern Physics, 3, Part I, 99, (1971).Google Scholar
  24. 19.
    Nakach, R.D., H. Wilhelmsson, Phys. Review Se ‘e A, (To be published July 1976 ).Google Scholar
  25. 20.
    Rosenbluth, M.N., B. Coppi, R. Sudan, Proc. J Intern. Conf. Plasma Physics and Contr. Nuclear Fusion Research, Novosibirsk, (1968).Google Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • R. Nakach
    • 1
  1. 1.Département de Physique du Plasma et de la Fusion Controlée Service IGn — Centre d’Etudes NucléairesAssociation Euratom-CEAGrenoble CedexFrance

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