Certain solutions of periodic long waves with non-linear dispersion

• Autorzy: Chybicki W.
• Języki publikacji: EN

Abstrakty

EN

The paper describes some special solutions of the long water waves theory proposed by Wilde. The wave equation is derived with the help of a variational formulation of the problem with the Langrangian being the difference between the kinetic and potential energies. In order to look for travelling wave solutions the simple transformation is made. The solutions have been found in the same way as in the KdV equation. Solutions for different wave amplitudes are presented in the paper. The special cases of solutions are solitary waves. It is proved that bounded solutions of an equation can represent periodic or solitary waves and both length and velocity of waves increase when the height of waves increases.

Słowa kluczowe

EN

long waves; Langrangian description

• Wydawca: Institute of Hydro-Engineering of Polish Academy of Sciences
• Czasopismo: Archives of Hydro-Engineering and Environmental Mechanics
• Rocznik: 2004
• Tom: Vol. 51, nr 4
• Strony: 307--315
• Opis fizyczny: Bibliogr. 6 poz., il.

Twórcy

autor

Chybicki W.

• Institute of Hydro-Engineering of the Polish Academy of Sciences, ul. Kościerska 7, 80-953 Gdańsk, Poland,

Bibliografia

• Massel S. (1989), Hydrodynamics of Coastal Zone, Elsevier Science Publ. Comp., Amsterdam.
• Pars L. A. (1964), Analytical Dynamics, Heineman, London
• Szmidt K. J. (2001), Third Order Approximation to Long Waves in Material Description, In: Zastosowania mechaniki w budownictwie ladowym i wodnym, Wydawnictwo IBW PAN Gdańsk (in Polish).
• Ursell F., (1953), The Long Wave Paradox in the Theory of Gravity Waves, Proc. Cambridge Philos, Soc., 49, 685–694.
• Whitham G. B. (1974), Linear and Non-linear Waves, J. Wiley & Sons, New York.
• Wilde P., Sobierajski E., Sobczak Ł.(2000), Laboratory Studies of the Influence of Generation on Long-Waves Properties (in Polish), internal report available at the library of the Institute.