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).
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References
N. Daher and G.A. Maugin, Acta Mechanica, 60 (1986), 217.
G.A. Maugin, in: Advances in applied Mechanics, ed. J.W. Hutchinson, Vol. 23, pp 373–434, Academic Press, New York (1983).
A.I. Murdoch, J. Mech. Phys. Solids, 24 (1976), 137.
G.A. Maugin, Nonlinear Electromechanical Effects and Applications, World Scientific, Singapore (1985), pp. 36–44.
H. Hadouaj and G.A. Maugin, C.R.Acad. Sci. Paris, II-309 (1989), 1877
G.A. Maugin and H. Hadouaj, Phys. Review, B (1991), in the press.
H. Hadouaj, G.A. Maugin, and B.A. Malomed, Phys. Review, B (1991).
H. Hadouaj, B.A. Malomed, and G.A. Maugin, Phys. Review, A (1991 a,b).
V.G. Mozhaev, Physics letters, A139 (1989), 333.
D.J. Benney and A.C. Newell, J. Math. and Phys., 46 (1967), 133
A.C. Newell, Solitons in Mathematics and Physics, S.I.A.M, Phil. (1985).
G.B. Whitham, Linear and Nonlinear Waves, J. Wiley, New York (1974)
W.D. Hayes, Proc. Roy. Soc. London, A320 (1970), 187.
V.E. Zakharov and A.B. Shabat, Sov. Phys. JETP., 34 (1972), 62; 37 (1973), 823.
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.
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.
Yu. S. Kivshar and B.A. Malomed, Rev. Mod. Phys., 61 (1989), 763.
A. Hasegawa, Optical Solitons in Fibers, Springer, Berlin (1989).
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.
G.A. Maugin and S. Cadet, Int. J. Engng. Sci, 29 (1991), 243.
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Hadouaj, H., Maugin, G.A., Malomed, B.A. (1991). Numerical results concerning the generalized Zakharov system. In: Remoissenet, M., Peyrand, M. (eds) Nonlinear Coherent Structures in Physics and Biology. Lecture Notes in Physics, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54890-4_191
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DOI: https://doi.org/10.1007/3-540-54890-4_191
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