Geodesic
Influence of cubic nonlinearity on the dispersion relation for long waves on a water surface
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 725-728 
A. V. Astashenok; A. A. Zaitsev. Influence of cubic nonlinearity on the dispersion relation for long waves on a water surface. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 725-728. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a14/
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     title = {Influence of cubic nonlinearity on the dispersion relation for long waves on a~water surface},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The influence of cubic nonlinearity on the dispersion relation for long waves on a water surface is analyzed. In the long wavelength limit, it is shown that the dispersion relation is not affected by the cubic terms. The results are compared with the dispersion relation for stationary solutions to the Korteweg–de Vries equation.

[1] Sretenskii L. H., Teoriya volnovykh dvizhenii idealnoi zhidkosti, Nauka, M., 1977

[2] Stoker Dzh., Volny na vode, Izd-vo inostr. lit., M., 1959

[3] Naife A. Kh., Teoriya vozmuschenii, Mir, M., 1976 | MR

[4] Fillips R., Dinamika verkhnego sloya okeana, Mir, M., 1969

[5] Uizem Dzh., Lineinye i nelineinye volny, Mir, M., 1977 | MR

[6] Lemb Dzh L., Vvedenie v teoriyu solitonov, Mir, M., 1983 | MR