Properties of a special function related to self-similar solutions of certain nonlinear wave equations

  • M. Leo
  • R. A. Leo
  • G. Soliani
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 120)


Some basic properties of a new special function pertinent to the study of certain nonlinear wave equations are presented.


Asymptotic Expansion Special Function Recurrence Relation Series Representation Nonlinear Wave Equation 
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  1. 1.
    M.Leo, R.A.Leo and G.Soliani, “On a special function related to a class of certain nonlinear wave equations”,1979, to be submitted for publication.Google Scholar
  2. 2.
    M.Leo, R.A.Leo and G.Soliani, “Some theorems concerning a new special function”, Quaderni dell'Istituto di Matematica dell'Università di Lecce, 1979.Google Scholar
  3. 3.
    A.C.Scott, F.Y.F.Chu and D.W.Mc Laughlin, “The soliton: a new concept in applied science”, Proceedings IEEE 61 (1973), pp.1443–1483.Google Scholar
  4. 4.
    V.G.Makhankov, “Dynamics of classical solitons (in non-integrable systems)”, Physics Reports 35 (1978), pp.1–128.Google Scholar
  5. 5.
    W.F.Ames, “Nonlinear ordinary differential equations in transport processes”, Academic Press, New York, 1968, p.42 and p.101.Google Scholar
  6. 6.
    H.T.Davis, “Introduction to nonlinear differential and integral equations”, Dover Publications, New York, 1962, p.20.Google Scholar
  7. 7.
    M.Abramowitz and I.A.Stegun, ”Handbook of mathematical functions”, Dover, New York, 1965, p.998.Google Scholar
  8. 8.
    F.W.J. Olver, “Asymptotic and special functions”, Academic Press, New York and London, 1974, p.25.Google Scholar
  9. 9.
    F.G.Tricomi, “Funzioni ipergeometriche confluenti”, Edizioni Cremonese, Roma, 1954, p.174.Google Scholar
  10. 10.
    I.S.Gradshteyn and I.M.Ryzhik, “Table of integrals, series and products”, Academic Press, N.Y., 1965, p.1075.Google Scholar
  11. 11.
    N.Ja.Vilenkin, “Fonctions spéciales et théorie de la représentation des groupes”, Dunod, Paris, 1969.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • M. Leo
    • 1
  • R. A. Leo
    • 1
  • G. Soliani
    • 1
  1. 1.Istituto di Fisica dell'Università di LecceLecceItaly

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