A note on solitary wave solutions of the Leibovich-Roberts equation

Bogdan, T. J.; Lerche, I.

doi:10.1090/qam/950608

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