The Conservation Laws and Stability of Fluid Waves of Permanent Form

Troyan A. Bodnar^{*}

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References

[1] T. A. Bodnar’, “One Approximate Solution of the Nekrasov Problem,” Journal of Applied Mechanics and Technical Physics, Vol. 48, No. 6, 2007, pp. 818-823.
doi:10.1007/s10808-007-0105-9

[2] T. A. Bodnar’, “On Steady Periodic Waves on the Surface of a Fluid of Finite Depth,” Journal of Applied Mechanics and Technical Physics, Vol. 52, No. 3, 2011, pp. 378-384.
doi:10.1134/S0021894411030072

[3] T. A. Bodnar’, “On Steady Waves on the Surface of a Finite-Depth Fluid,” Free Boundary Problems: Theory, Experiment, and Applications, 3rd All-Russian Conference with International Participation, Biisk, 28 June-3 July 2008, pp. 25-26.

[4] A. I. Nekrasov, “Exact Theory of Steady Waves on the Surface of a Heavy Fluid,” Izd.Akad.Nauk SSSR, Moskow, 1951. (In Russian)

[5] R. Courant and D. Hilbert, “Methods of Mathematical Physics,” Interscience, New York, 1953.

[6] G. A. Chandler and I. G. Graham, “The Computation of Water Waves Modelled by Nekrasov’s Equation,” SIAM Journal on Numerical Analysis, Vol. 30, 1993, pp. 1041-1065. doi:10.1137/0730054

[7] R. Courant, “Differential and Integral Calculus,” Interscience, New York,1936.

[8] L. N. Sretenskii, “Theory of Fluid Wave Motion,” Nauka, Moscow, 1977. (In Russian)

[9] T. A. Bodnar’, “Conservation Law of the Full Mechanical Energy and Stability of the Steady-State Waves on the Surface of a Fluid of Finite Depth,” In: IV All-Russian Conference with foreign participation on Free Boundary Problems: Theory, Experiment, and Applications, Biisk, 5-10 July 2011, pp. 18-19.