Abstract
The concepts of the theory of nonlinear waves are briefly analyzed. Two examples are given characterizing the nonlinear effects in wave propagation. The first deals with short-living solitary waves in a dispersive medium and the second with interaction of two-dimensional nonlinear waves.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Engelbrecht, J.: Nonlinear Wave Dynamics: Complexity and Simplicity, Kluwer Acad. Publ., Dordrecht, 1997.
Zabusky, N.J.: Acta Appl. Math. 39 (1995), 159–172.
Jeffrey, A., and Engelbrecht, J.: (eds) Nonlinear Waves in Solids, Springer, Wien et al., 1994.
Engelbrecht, J.: Shock and Vibr. 2 (1995), 173–190.
Engelbrecht, J., and Braun, M.: Appl. Mech. Rev. 51 (1998), 475–488.
Christov, C.I., Maugin, G.A., and Velarde, M.G.:Phys. Rev. 54 (1996), 3621–3638.
Salupere, A., Maugin, G.A., and Engelbrecht, J.: Proc. Estonian Acad. Sci. Phys. Math. 46 (1997), 1/2, 118–127.
Naumkin, P.I., and Shishmarev, I.A.: Nonlinear Nonlocal Equation in the Theory of Waves. AMS, Providence, 1994.
Maugin, G.A., Collet, B., Dronot, R., and Pouget J.: Nonlinear Electromechanical Couplings. J.Wiley, Chicester et al., 1992.
Lebon, G., Jou, D., and Casas-Vazquez J.: Contemporary Physics 33 (1992), 41–51.
Maugin, G.A.: J. Non-Equilib. Thermodyn. 15 (1990), 173–192.
Whitham G.B.: Linear and Nonlinear Waves. J. Wiley, New York et al., 1974.
Engelbrecht, J., Pastrone, F., and Cermelli, P.: Wave hierarchy in microstructured solids. In G.A.Maugin (ed.) Geometry, Mechanics, Microstructure. Hermann Publ., Paris (to be published in 1998).
Stronge, W.: Proc. Roy Soc. London A 409 (1987), 199–208.
Kyriakides, S.: Adv. Appl. Mech. 30 (1993), 67–189.
Zabusky, N.J., and Kruskal, M.D.: Phys. Rev. Lett. 15 (1965), 240–243.
Abe, K., and Abe, T.: Phys.,Fluids 22 (1979), 1644–1646.
Salupere, A., Maugin, G.A., Engelbrecht, J., and Kalda J.: Wave Motion 23 (1996), 49–66.
Grammaticos, B., Ramani, A., and Hietarinta, J.: J. Math. Phys. 31(11) (1990), 2572–2578.
Hirota, R.: Direct methods in soliton theory. In R.K. Bullough and P.J. Gaudrey, (eds), Solitons. Springer, Berlin et al. (1980), 157–176.
Freeman, N.C.: Adv. in Appl. Mech. 20 (1980), 1–37.
Peterson, P.: I. Interaction of KdV-type solitons in terms of phase variables. Interaction soliton. Research Report 185/98, Inst. of Cybernetics, April 1998.
Peterson, P.: II. Interaction of KdV-type solitons in terms of real space and time variables. Research Report 186/98, Inst. of Cybernetics, May 1998.
Miles, J.W.: J. Fluid Mech. 79(1) (1977), 171–179.
Johnson, R.S.: J. Fluid Mech 323 (1996), 65–78.
Hammack, J., McCallister, D., Scheffner, N., and Segur, H.: J. Fluid Mech 285 (1995), 95–122.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Engelbrecht, J., Salupere, A., Peterson, P. (2000). Nonlinear Wave Motion: Complexity and Simplicity Revisited. In: Lavendelis, E., Zakrzhevsky, M. (eds) IUTAM / IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems. Solid Mechanics and its Applications, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4229-8_3
Download citation
DOI: https://doi.org/10.1007/978-94-011-4229-8_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5836-0
Online ISBN: 978-94-011-4229-8
eBook Packages: Springer Book Archive