Keywords
- Solitary Wave
- Cnoidal Wave
- Nonlinear Wave Motion
- Steady Periodic 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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
T. B. Benjamin, 1967 ‘Internal waves of permanent form in fluids of great depth’, J. Fluid Mech. 29, p. 559.
-, 1971, ‘A unified theory of conjugate flows’, Philos. Trans. Roy. Soc. London Ser. A. 269, p. 587.
-, 1972 ‘The stability of solitary waves’, Proc. Roy. Soc. London Ser A. 328, p. 153.
T. B. Benjamin, 1974 ‘Lectures on nonlinear wave motion’, Nonlinear Wave Motion (Proceedings of the Summer Seminar Potsdam, New York, 1972), p. 3, Ammerican Math. Society, Lectures in Applied Mathematics Vol 15.
T. B. Benjamin, J. L. Bona and J. J. Mahony, 1972 ‘Model equations for long waves in nonlinear dispersive systems’, Philos. Trans. Roy. Soc. London Ser. A. 272, p. 47.
J. L. Bona, 1975, ‘On the stability theory of solitary waves’, Proc. Roy. Soc. London Ser. A 344, p. 363.
J. L. Bona and D. K. Bose, 1974 ‘Fixed point theorems for Fréchet spaces and the existence of solitary waves’, Nonlinear Wave Motion (Proceedings of the Summer Seminar, Potsdam, New York, 1972) p. 175, American Math. Society, Lectures in Applied Mathematics Vol 15.
J. Boussinesq, 1871 ‘Théorie de l’intumescence liquide appelée onde solitaire ou de translation se propageant dans un canal rectangulaire’, Comptes Rendus 72, 755.
K. O. Friedricks and D. H. Hyers, 1954. ‘The existence of solitary waves’, Comm. Pure Appl. Math. 7, p. 517.
C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, 1967, ‘Method for solving the Korteweg-de Vries equation’, Phys. Rev. Letters 19, p. 1095.
-, 1974. ‘Korteweg-de Vries equation and generalizations’, VI. Methods for exact solution Comm. Pure Appl. Math 27, p. 27.
J. L. Hammack, 1973, ‘A note on tsunamis: their generation and propagation in an ocean of uniform depth’, J. Fluid Mech. 60, p. 769.
J. L. Hammack and H. Segur, 1974 ‘The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments’, J. Fluid Mech. 65, p. 289.
D. J. Korteweg and G. De Vries, 1895 ‘On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves’, Philos. Mag (5) 39, p. 422.
S. Leibovich, 1970, ‘Weakly nonlinear waves in rotating fluids’, J. Fluid Mech. 42, p. 803.
S. Leibovich and J. D. Randall, 1972, ‘Solitary waves in concentrated vortices’, J. Fluid Mech. 51, p. 625.
W. G. Pritchard, 1969 ‘The motion generated by a body moving along the axis of a uniformly rotating fluid’, J. Fluid Mech. 39, p. 443.
-, 1970 ‘Solitary waves in rotating fluid’, J. Fluid Mech. 42, p. 61.
Lord Rayleigh, 1876 ‘On waves’, Philos Mag (5) 1, p. 257.
J. Scott Russell, 1844 ‘Report on waves’, Rep. Fourteenth Meeting of the British Assoc., John Murray, London, p. 311.
R. Smith, 1972 ‘Nonlinear Kelvin and continental-shelf waves’, J. Fluid Mech. 57, p. 393.
M. M. Vainberg, 1964 Variational methods for the study of nonlinear operators, Holden-Day, San Francisco, Calif.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1976 Springer-Verlag
About this paper
Cite this paper
Bona, J.L., Bose, D.K., Benjamin, T.B. (1976). Solitary-wave solutions for some model equations for waves in nonlinear dispersive media. In: Germain, P., Nayroles, B. (eds) Applications of Methods of Functional Analysis to Problems in Mechanics. Lecture Notes in Mathematics, vol 503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088757
Download citation
DOI: https://doi.org/10.1007/BFb0088757
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07629-2
Online ISBN: 978-3-540-38165-5
eBook Packages: Springer Book Archive
