caa a22 4500 386372284 CHVBK 20180307112002.0 cr unu---uuuuu 161130e198905 xx s 000 0 eng 10.1017/S0017089500007667 doi S0017089500007667 pii (NATIONALLICENCE)cambridge-10.1017/S0017089500007667 Jones M. C. W. Department of Pure Mathematics, The Queen's University of Belfast, Belfast BT7 INN. Northern Ireland., U. K. Small amplitude capillary-gravity waves in a channel of finite depth [Elektronische Daten] [M. C. W. Jones] Introductory Remarks. Recently a number of studies (Chen & Saffman [2], Jones & Toland [7,11], Hogan [5]) have been made of periodic capillary-gravity waves which form the free surface of an ideal fluid contained in a channel of infinite depth. However, little work appears to have been done on the corresponding problem when the depth is finite. The most significant contributions appear to be those of Reeder & Shinbrot [9], Barakat & Houston [1] and Nayfeh [8] all of whom confined themselves to Wilton ripples (see §1.3). Yet there are sound reasons why such a study should be made. For quite apart from the unsolved problem regarding the type of capillary-gravity waves which may occur at finite depths, the consideration of the finite depth problem may be regarded as a first step in the study of solitary capillary-gravity waves. In this paper, a new integral equation for the infinite depth problem, due to J. F. Toland and the author, is adapted to be of use in tackling the finite depth problem. Using this we obtain results for the exact equations of motion which answer rigorously the questions of existence and multiplicity of small amplitude solutions of the periodic capillary-gravity wave problem of finite depth. Copyright © Glasgow Mathematical Journal Trust 1989 Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 142-160 0017-0895 31:2<142 1989 31 GMJ https://doi.org/10.1017/S0017089500007667 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0017089500007667 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jones M. C. W. Department of Pure Mathematics, The Queen's University of Belfast, Belfast BT7 INN. Northern Ireland., U. K NATIONALLICENCE 773 0- Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 142-160 0017-0895 31:2<142 1989 31 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge