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Instability of waveguides in a liquid with surface effects. (English. Russian original) Zbl 1161.76349
Fluid Dyn. 37, No. 6, 919-930 (2002); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2002, No. 6, 81-92 (2002).
Summary: Long surface capillary-gravity waves and waves beneath an elastic plate simulating an ice sheet are considered for a liquid of finite depth. These waves are described by a generalized Kadomtsev-Petviashvili equation containing higher (as compared with the ordinary Kadomtsev-Petviashvili equation) space derivatives. The generalized Kadomtsev-Petviashvili equation has waveguide solutions (waveguides) corresponding to traveling waves which are periodic in the direction of propagation and localized in the transverse direction. These waves result from the instability of uniform (carrier) periodic waves with respect to transverse perturbations. The stability of the waveguides with respect to longitudinal longwave perturbations is studied. The behavior of these perturbations depends on the wavenumber of the carrier periodic wave. Three intervals of wavenumbers corresponding to all the possible types of governing equations are considered.
MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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