Uniqueness of Crapper's pure capillary waves of permanent shape

J. Math. Sci. Univ. Tokyo
Vol. 12 (2005), No. 1, Page 67--75.

Okamoto, Hisashi
Uniqueness of Crapper's pure capillary waves of permanent shape
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Abstract:
Two-dimensional water-waves of permanent shape with constant propagation speed are considered under the assumption that the gravity is neglected and only the surface tension is taken into account. Crapper's solutions, which are exact solutions of the governing equations, are proved to be unique among those which satisfy a certain positivity property.

Keywords: Crapper's wave, uniqueness, positivity

Mathematics Subject Classification (1991): Primary 76B45, Secondary 34B15
Mathematical Reviews Number: MR2126785

Received: 2003-10-21