Geodesic
The solution of a nonlinear problem of waves on the surface weakly-viscous fluid
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 2 (2011), pp. 9-16

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The nonlinear problem about propagation of gravitational waves on a free surface weakly-viscous fluid is considered. It is offered to consider viscous dissipation not only in speed of wave motion of a fluid, but also in wave parameters – frequency and decrement of attenuation of a wave. Therefore wave parameters are set as functions a subject definition from time. Such representation has allowed to apply effectively to the decision of a nonlinear problem a method of successive approximations of Stokes. The solution is found with accuracy of the third approach. The received expressions for frequency and decrement of attenuation of a wave represent the sum of two composed. The first – a constant corresponding a linear problem. The second composed, considering nonlinear effects – function of time, eventually aspiring zero. The found expressions in neglect viscosity pass all in known for an perfect fluid.
Keywords: nonlinear surface waves, viscosity of a fluid, the dispersion relations. 
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     author = {V. A. Barinov and K. Yu. Basinsky},
     title = {The solution of a nonlinear problem of waves on the surface weakly-viscous fluid},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {9--16},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2011_2_a1/}
}
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V. A. Barinov; K. Yu. Basinsky. The solution of a nonlinear problem of waves on the surface weakly-viscous fluid. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 2 (2011), pp. 9-16. http://geodesic.mathdoc.fr/item/VSPUI_2011_2_a1/