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Exact solitary water waves with capillary ripples at infinity
Author(s) -
Beale J. Thomas
Publication year - 1991
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160440204
Subject(s) - inviscid flow , oscillation (cell signaling) , mathematics , infinity , surface tension , crest , mathematical analysis , capillary wave , scale (ratio) , amplitude , flow (mathematics) , free surface , mechanics , physics , geometry , optics , genetics , quantum mechanics , biology
We prove the existence of solitary water waves of elevation, as exact solutions of the equations of steady inviscid flow, taking into account the effect of surface tension on the free surface. In contrast to the case without surface tension, a resonance occurs with periodic waves of the same speed. The wave form consists of a single crest on the elongated scale with a much smaller oscillation at infinity on the physical scale. We have not proved that the amplitude of the oscillation is actually nonzero; a formal calculation suggests that it is exponentially small.