Geodesic
About the stability of branching solutions in the problem on capillary-gravity waves in a~deep spatial layer of floating fluid
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2009), pp. 10-25

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Potential flows of incompressible heavy capillary floating fluid in free-dimensional layer of infinite depth with free upper boundary are determined. Asymptotics of periodical flows in spatial layer with free upper boundary close to horizontal plane $z=0$ bifurcating from the basic flow with constant velocity $V$ in $Ox$-direction are calculated. Their orbital stability relative to pertubations of the same symmetry is investigated. Methods of group-invariant bifurcation theory and group analysis of differential equations are used. Special attention is given to cases of high-dimensional ($n \ge 4$) degeneration of the linearized operator.
Keywords: floating deep fluid layer, capillary-gravity surface waves, branching, stability, group symmetry. 
@article{VSGU_2009_2_a1,
     author = {A. N. Andronov},
     title = {About the stability of branching solutions in the problem on capillary-gravity waves in a~deep spatial layer of floating fluid},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {10--25},
     publisher = {mathdoc},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2009_2_a1/}
}
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A. N. Andronov. About the stability of branching solutions in the problem on capillary-gravity waves in a~deep spatial layer of floating fluid. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2009), pp. 10-25. http://geodesic.mathdoc.fr/item/VSGU_2009_2_a1/