Stability of bifurcating solutions of the problem about capillary-gravity surface waves in spatial layer of floating fluid |
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| Authors: | Artyom N. Andronov Luiza R. Kim-Tyan Boris V. Loginov |
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| Affiliation: | 1. Mordovian State University, Saransk, Russia;2. Moscow Institute of Steel and Allows, Moscow, Russia;3. Chair of Higher Mathematics, Ulyanovsk State Technical University, Ulyanovsk, Russia |
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| Abstract: | In prolongation of our previous investigations on capillary-gravity surface waves in spatial fluid layers the stability of the bifurcating families of solutions in the horizontal layers of the floating (and without flotation) incompressible heavy capillary fluid is considered. The assumption about layer depth simplifies the proof of the existence of bifurcating solutions at the high dimensions of the linearized operator degeneracy, computation of their asymptotics and as the main subject of this communication the investigation of their stability, relative to perturbations with the same symmetry as bifurcating solutions. Group analysis methods of differential equations are used. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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