Abstract
This chapter is an introduction to nonlinear waves in dispersive media. We show how the interaction of nonlinear and nonlocal effects leads to such basic phenomenon as the soliton.
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References
D.J. Korteweg, G. deVries: On the change of form of long waves advancing in a rectangular channel, and on a new type of long stationary waves. Philos. Mag. 39, 422–443 (1895)
V.I. Karpman: Non-linear Waves in Dispersive Media ( Pergamon, Oxford 1975 )
M.M. Vainberg: Variational Methods for the Study of Non-linear Operators ( Holden-Day, San Francisco 1964 )
I.M. Gel’fand, S.V. Fomin: Calculus of Variation ( Prentice-Hall, Englewood Cliffs, NJ 1963 )
M. Toda: Wave in nonlinear lattice. Prog. Theor. Phys. 45,174–200 (1970) [Supplement]
M. Toda: Theory of Nonlinear Lattices, Springer Series in Solid-State Sci., Vol. 20 ( Springer, Berlin, Heidelberg, New York 1981 )
N. Ooyama, N. Saito: On the stability of lattice solitons. Prog. Theor. Phys. 45,201–208 (1970) [Supplement]
N.J. Zabusky: Solitons and bound states of the time-independent Schrödinger equation. Phys. Rev. 168, 124–128 (1968)
R. Hirota: Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices. J. Math. Phys. 14, 810–814 (1973)
M.Y. Beran: Statistical Continuum Theories ( Interscience, New York 1968 )
V.E. Zakharov: Kinetic equation for solitons. Sov. Phys. JETP 33, 538–541 (1971)
A. Seeger: „Zur Dynamik von Versetzungen in Gitterreihen mit verschiedener Gitterkonstanten“; Thesis, Technische Hochschule Stuttgart (1948–49)
A. Kochendorfer, A. Seeger: Theorie der Versetzungen in eindimensionalen Atomreihen. I. Periodisch angeordnete Versetzungen. Z. Phys. 127, 533–550 (1950)
A. Seeger, H. Donth, A. Kochendorfer: Theorie der Versetzungen in eindimensionalen Atomreihen. III. Versetzungen, Eigenbewegungen und ihre Wechselwirkung. Z. Phys. 134,173–193 (1953)
A. Seeger: “Solitons in Crystals”, in Continuum Models of Discrete Systems (CMDS3), ed. by E. Kroner, K.H. Anthony (Univ. Waterloo Press 1980 ) pp. 253–327
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© 1982 Springer-Verlag Berlin Heidelberg
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Kunin, I.A. (1982). Nonlinear Waves. In: Elastic Media with Microstructure I. Springer Series in Solid-State Sciences, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81748-9_5
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DOI: https://doi.org/10.1007/978-3-642-81748-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-81750-2
Online ISBN: 978-3-642-81748-9
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