Two-dimensional wave packets in an elastic solid with couple stresses

International Journal of Non-Linear Mechanics

Volumn 39, Issue 6, 2004, Pages 941-949

  Babaoglu, Ceni ^a   Erbay, Saadet ^b  

^a ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

^b ISIK UNIVERSITY   (Turkey)

Author keywords

Generalized Davey Stewartson equations; Non linear elastic wave propagation

Indexed keywords

ELASTICITY; FUNCTIONS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; POLYCRYSTALLINE MATERIALS; STRESSES; WAVE EQUATIONS; WAVE PROPAGATION;

ELASTIC WAVE PROPAGATION; GENERALIZED DAVEY-STEWARTSON (GDS) EQUATIONS;

ELASTIC WAVES;

EID: 0345306161     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(03)00076-3     Document Type: Article

References (21)

1. Dodd R.K., Eilbeck J.C., Gibbon J.D., Morris H.C. Solitons and Nonlinear Wave Equations. 1982;Academic Press, London.
2. Hasegawa A. Optical Solitons in Fibers. 1989;Springer, Berlin.
3. Ablowitz M.J., Clarkson P.A. Solitons, Nonlinear Evolution Equations and Inverse Scattering. 1992;Cambridge University Press, Cambridge.
4. Taniuti T., Yajima N. Perturbation method for a nonlinear wave modulation. I. J. Math. Phys. 10:1969;1369.
5. Pouget J., Remoissenet M., Tamga J.M. Energy self-localization and gap local pulses in a two-dimensional nonlinear lattice. Phys. Rev. B. 47:1993;14866.
6. Collet B., Pouget J. Two dimensional modulation and instabilities of flexural waves of a thin plate on nonlinear elastic foundation. Wave Motion. 27:1998;341.
7. Davey A., Stewartson K. On three dimensional packets of surface waves. Proc. Roy. Soc. London Ser. A. 338:1974;101.
8. Djordjevic V.D., Redekopp L.G. On two-dimensional packets of capillary-gravity waves. J. Fluid Mech. 79:1977;703.
9. Ablowitz M.J., Segur H. On the evolution of packets of water waves. J. Fluid Mech. 92:1979;691.
10. Kovriguine D.A., Potapov A.I. Nonlinear waves in elastic bar. Eur. J. Mech. A/Solids. 15:1996;1049.
11. Maugin G.A., Hadouaj H., Malomed B.A. Nonlinear coupling between shear horizontal surface solitons and Rayleigh modes on elastic structures. Phys. Rev. B. 45:1992;9688.
12. Mayer A.P. Surface acoustic waves in nonlinear elastic media. Phys. Rep. 256:1995;237.
13. Maugin G.A. Nonlinear Waves in Elastic Crystals. 1999;Oxford University Press, Oxford.
14. Jeffrey A., Engelbrecht J. Nonlinear Waves in Solids. 1994;Springer, New York.
15. Engelbrecht J. Nonlinear Wave Dynamics, Complexity and Simplicity. 1997;Kluwer Academic Publishers, Dordrecht.
16. Babaoglu C., Erbay S. Two-dimensional wave propagation in a generalized elastic solid. Chaos, Solitons Fractals. 12:2001;381.
17. Suhubi E.S., Eringen A.C. Nonlinear theory of micro-elastic solids - II. Int. J. Eng. Sci. 2:1964;389.
18. Erofeyev V.I., Potapov A.I. Longitudinal strain waves in non-linearly elastic media with couple stresses. Int. J. Non-Linear Mech. 28:1993;483.
19. Taniuti T. Reductive perturbation methods and far fields of wave equation. Prog. Theor. Phys. Suppl. 55:1974;1.
20. Byrd P.F., Friedman M.D. Handbook of Elliptic Integrals for Engineers and Physicists. 1954;Springer, Berlin.
21. C. Babaoglu, A. Eden, S. Erbay, A blow-up result for a Generalized Davey-Stewartson system, 2003, submitted for publication.