Advertisement

Numerical results concerning the generalized Zakharov system

  • Hichem Hadouaj
  • Gérard A. Maugin
  • Boris A. Malomed
Part VI: Mathematical Methods
  • 172 Downloads
Part of the Lecture Notes in Physics book series (LNP, volume 393)

Abstract

A generalization of the well known Zakharov system of ionacoustic waves (Langmuir solitons) has been obtained while studying the coupling between shear-horizontal surface waves and Rayleigh surface waves propagating on top of a structure made of a nonlinear elastic substrate and a superimposed thin elastic film. The generalization consists in a nearly integrable system made of a nonlinear Schrödinger equation (thus including self-interactions) coupled to two wave equations for the secondary acoustic system (Rayleigh mode). Here we present essentially the numerical simulations pertaining to the uncoupled case (pure SH mode) and the coupled case (influence of viscous dissipation in the Rayleigh subsystem, collision of solitons).

Keywords

Linear Dispersion Relation Rayleigh Surface Wave Zakharov System Rayleigh Mode Envelope Solitary Wave 
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.

References

  1. [1]
    N. Daher and G.A. Maugin, Acta Mechanica, 60 (1986), 217.CrossRefGoogle Scholar
  2. [2]
    G.A. Maugin, in: Advances in applied Mechanics, ed. J.W. Hutchinson, Vol. 23, pp 373–434, Academic Press, New York (1983).Google Scholar
  3. [3]
    A.I. Murdoch, J. Mech. Phys. Solids, 24 (1976), 137.CrossRefGoogle Scholar
  4. [4]
    G.A. Maugin, Nonlinear Electromechanical Effects and Applications, World Scientific, Singapore (1985), pp. 36–44.Google Scholar
  5. [5]
    H. Hadouaj and G.A. Maugin, C.R.Acad. Sci. Paris, II-309 (1989), 1877Google Scholar
  6. [5a]
    G.A. Maugin and H. Hadouaj, Phys. Review, B (1991), in the press.Google Scholar
  7. [6]
    H. Hadouaj, G.A. Maugin, and B.A. Malomed, Phys. Review, B (1991).Google Scholar
  8. [7]
    H. Hadouaj, B.A. Malomed, and G.A. Maugin, Phys. Review, A (1991 a,b).Google Scholar
  9. [8]
    V.G. Mozhaev, Physics letters, A139 (1989), 333.Google Scholar
  10. [9]
    D.J. Benney and A.C. Newell, J. Math. and Phys., 46 (1967), 133Google Scholar
  11. [9a]
    A.C. Newell, Solitons in Mathematics and Physics, S.I.A.M, Phil. (1985).Google Scholar
  12. [10]
    G.B. Whitham, Linear and Nonlinear Waves, J. Wiley, New York (1974)Google Scholar
  13. [10a]
    W.D. Hayes, Proc. Roy. Soc. London, A320 (1970), 187.Google Scholar
  14. [11]
    V.E. Zakharov and A.B. Shabat, Sov. Phys. JETP., 34 (1972), 62; 37 (1973), 823.Google Scholar
  15. [12]
    H. Hadouaj and G.A. Maugin, in: Mathematical and Numerical Aspects of Wave Propagation, S.I.A.M, Philadelphia (1991); Wave Motion (Special issue on “ Nonlinear Waves in Deformable Solids ”. I.C.I.A.M'91, Washington, D.C), 14,(1991) in the press.Google Scholar
  16. [13]
    V.E. Zakharov, Sov. Phys. JETP, 35 (1972), 908; E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos, Cambridge University Press, U.K (1990), PP. 319–321.Google Scholar
  17. [14]
    Yu. S. Kivshar and B.A. Malomed, Rev. Mod. Phys., 61 (1989), 763.CrossRefGoogle Scholar
  18. [15]
    A. Hasegawa, Optical Solitons in Fibers, Springer, Berlin (1989).Google Scholar
  19. [16]
    G.A. Maugin and A. Miled, Phys. Rev., B33 (1986), 4830; J.Pouget and G.A. Maugin, Phys. Rev., B30 (1984), 5306; ibid, B31 (1985), 4633.Google Scholar
  20. [17]
    G.A. Maugin and S. Cadet, Int. J. Engng. Sci, 29 (1991), 243.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Hichem Hadouaj
    • 1
  • Gérard A. Maugin
    • 1
  • Boris A. Malomed
    • 1
  1. 1.Laboratoire de Modélisation en Mécanique associé au C.N.R.S.Université Pierre-et-Marie CurieParis Cédex 05France

Personalised recommendations