MacKay, R. S. and Saffman, P. G. (1986) Stability of Water Waves. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 406 (1830). pp. 115-125. ISSN 1364-5021. doi:10.1098/rspa.1986.0068. https://resolver.caltech.edu/CaltechAUTHORS:20150128-142455198
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Abstract
We apply some general results for Hamiltonian systems, depending on the notion of signature of eigenvalues, to determine the circumstances under which collisions of imaginary eigenvalue for the linearized problem about a travelling water wave of permanent form are avoided or lead to loss of stability, up to non-degeneracy assumptions. A new superharmonic instability is predicted and verified.
| Item Type: | Article | ||||||||||||
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| Additional Information: | © 1986 The Royal Society. Received 31 January 1986. We thank the London Mathematical Society and the Science and Engineering Research Council for sponsoring the 1984 Durham Bifurcation Theory Symposium, which stimulated this work. P. G. S. also thanks the Office of Naval Research (N00014-79-C-0412, NR062-639) for support, and R. S. M. the Nuffield Foundation for travel expenses to discuss this work. Last, but not least, thanks to Peta McAllister for typing the paper. | ||||||||||||
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| Issue or Number: | 1830 | ||||||||||||
| DOI: | 10.1098/rspa.1986.0068 | ||||||||||||
| Record Number: | CaltechAUTHORS:20150128-142455198 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150128-142455198 | ||||||||||||
| Official Citation: | Stability of Water Waves Author(s): R. S. MacKay and P. G. Saffman Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 406, No. 1830 (Jul. 8, 1986), pp. 115-125 Published by: The Royal Society Stable URL: http://www.jstor.org/stable/2397813 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 54196 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | INVALID USER | ||||||||||||
| Deposited On: | 28 Jan 2015 23:18 | ||||||||||||
| Last Modified: | 10 Nov 2021 20:30 |
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