الفهرس 
Water wavesOnly 14 pages are availabe for public view
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Abstract
This thesis contains four chapters organized as follows: the introduction, three
chapters, Arabic summary and a list of references and links. It is concerned with the
study of the solutions of some problems in water waves. Shallow water equations can
be used to model Rossby and Kelvin waves in the atmosphere, rivers, lakes and
oceans as well as gravity waves in a smaller domain (e.g. surface waves in a bath). In
order for shallow water equations to be valid, the wavelength of the phenomenon they
are supposed to model has to be much higher than the depth of the basin where the
phenomenon takes place. Shallow water equations are especially suitable to model
tides which have very large length scales (over hundred of kilometers). For tidal
motion, even a very deep ocean may be considered as shallow as its depth will always
be much smaller than the tidal wavelength. In coastal engineering, Shallow water
equations are frequently used in computer models for the simulation of water waves
in shallow seas and harbors. Analytical solutions of the nonlinear partial differential
equations, which governing the water wave problem, are investigated for long waves
in shallow water by using various methods. Moreover, this study presents the material
in a way that emphasizes the mathematical aspects of classical water wave problems,
and indicates a description of the intrinsic relation between soliton types and water
waves for instance. We discuss the fundamental properties of the solutions and
making comparison with the physical situations and the previous works.