Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T14:03:10.922Z Has data issue: false hasContentIssue false
  • English
  • Français

Some numerical solutions of a variable-coefficient Korteweg-de Vries equation (with applications to solitary wave development on a shelf)

Published online by Cambridge University Press:  29 March 2006

R. S. Johnson
R. S. Johnson
Affiliation:
School of Mathematics, University of Newcastle upon Tyne
Get access Rights & Permissions [Opens in a new window]

Abstract

Some numerical solutions of a variable-coefficient Korteweg-de Vries equation are presented. This particular equation was derived by the author recently (Johnson 1972) in an attempt to describe the development of a single solitary wave moving onto a shelf. Soliton production on the shelf was predicted and this is confirmed here. Results for two and three solitons are reproduced and two intermediate shelf depths are also considered. In these latter two cases both solitons and an oscillatory wave occur. One of the profiles corresponds to the integrations performed by Madsen & Mei (1969) and a comparison is made.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 1 , 11 July 1972 , pp. 81 - 91
Copyright
© 1972 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benjamin, T. B., Bona, J. L. & Mahony, J. J. 1971 Fluid Mechanics Research Institute, University of Essex Rep. no. 13.
Johnson, R. S. 1972 to appear, Proc. Camb. Phil. Soc.
Korteweg, D. J. & de Vries, G. 1895 Phil. Mag. 39 (5), 433
Madsen, O. S. & Mei, C. C. 1969 J. Fluid Mech. 39, 781.
Miura, R. M., Gardener, C. S. & Kruskal, M. D. 1968 J. Math. Phys. 9, 1204.
Miura, R. M., Gardener, C. S. & Kruskal, M. D. 1969 J. Math. Phys. 10, 536.
Miura, R. M., Gardener, C. S. & Kruskal, M. D. 1970 J. Math. Phys. 11, 1952.
Tappert, F. D. & Zabusky, N. J. 1971 Gradient induced fission of solitons. Submitted to Phys. Rev. Lett.Google Scholar
Vliegenthart, A. C. 1971 J. Engng. Math. 5, 137
Zabusky, N. J. 1968 Phys. Rev. 168, 124.
Zabusky, N. J. & Galvin, C. J. 1971 J. Fluid Mech. 47, 811.
Zabusky, N. J. & Kruskal, M. D. 1965 Phys. Rev. Lett. 15, 240.