An equation for stationary capillary gravitational-gyroscopic waves in shallow water, and Kelvin waves
Itogi nauki i tehniki. Seriâ, Matematičeskij analiz, Itogi Nauki i Tekhniki. Seriya "Matematicheskii Analiz", Tome 24 (1986), pp. 207-269
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On the basis of a spectral asymptotic method developed by the authors, a rigorous derivation is given on the equation of capillary waves on shallow water with consideration of the rotation of the fluid and its stratification. The character of the wave motions described by this equation is investigated, and the existence of capillary Kelvin waves is established. Moreover, the problem of the diffraction of these waves by a half plane is studied.
@article{INTM_1986_24_a2,
     author = {S. A. Gabov and A. G. Sveshnikov},
     title = {An equation for stationary capillary gravitational-gyroscopic waves in shallow water, and {Kelvin} waves},
     journal = {Itogi nauki i tehniki. Seri\^a, Matemati\v{c}eskij analiz},
     pages = {207--269},
     year = {1986},
     volume = {24},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTM_1986_24_a2/}
}
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S. A. Gabov; A. G. Sveshnikov. An equation for stationary capillary gravitational-gyroscopic waves in shallow water, and Kelvin waves. Itogi nauki i tehniki. Seriâ, Matematičeskij analiz, Itogi Nauki i Tekhniki. Seriya "Matematicheskii Analiz", Tome 24 (1986), pp. 207-269. http://geodesic.mathdoc.fr/item/INTM_1986_24_a2/