|
Online ISSN 1552-4485; Print ISSN 0033-569X
A note on solitary wave solutions of the Leibovich-Roberts equation
Authors:
T. J. Bogdan and I. Lerche
Journal:
Quart. Appl. Math. 46 (1988), 365-374
MSC:
Primary 76B25; Secondary 35Q20
DOI:
https://doi.org/10.1090/qam/950608
MathSciNet review:
950608
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The propagation of weakly nonlinear, weakly dispersive sound waves in a magnetic cylinder satisfies an equation originally discussed in a limiting form by Leibovich (1970) and in general form by Roberts (1985). We show here that the resulting Leibovich-Roberts equation possesses nonlinear solitary wave behaviors akin to Benjamin-Ono waves in a slab. We also show how the structure of the solitary waves can be determined using a variational principle.
-
M. Becker, The Principles and Applications of Variational Methods, M.I.T., Cambridge, 1964
- S. Leibovich, Weakly non-linear waves in rotating fluids, J. Fluid Mech. 42 (1970), 803–822. MR 273890, DOI https://doi.org/10.1017/S0022112070001611 P. M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill Book Co., New York, 1963 B. Roberts, Solitary waves in a magnetic fluxtube, Phys. Fluids 28, 3280–3286 (1985)
- F. G. Tricomi, Integral equations, Pure and Applied Mathematics, Vol. V, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR 0094665
Retrieve articles in Quarterly of Applied Mathematics with MSC: 76B25, 35Q20
Retrieve articles in all journals with MSC: 76B25, 35Q20
Additional Information
Article copyright:
© Copyright 1988
American Mathematical Society