الفهرس | Only 14 pages are availabe for public view |
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. |