On periodic water-waves and their convergence to solitary waves in the long-wave limit
- 24 December 1981
- journal article
- Published by The Royal Society in Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- Vol. 303 (1481) , 633-669
- https://doi.org/10.1098/rsta.1981.0231
Abstract
A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).Keywords
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