الفهرس 
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Abstract
Over the past decades a great deal of attention has given to internal wave problems between two fluids either rigid or free upper boundary due to their
Several methods, both experimental theoretical are used to solve these problems.
In this thesis, the main mathematical methods used in e field of fluid mechanics are reviewed and a special
upon methods used in solving internal wave
All problems in this thesis are solved under the
influence of gravity is considered, e two-fluid system is statically stable, the fluids being
incompressible and that the flow is o-dimensional, irrotational, steady and finally that the
tension at the surface of separation of as well as the interface thickness has been
Three different internal wave problems are solved in thesis, namely: The problem of determining the shape
solitary wave in a two-fluid system of topography, the problem of time-dependent gravity waves with rigid upper boundary over topography and finally the problem of internal gravity waves with free upper irregular topography. In the latter problem profile of the free surface wave has been also
first problem, a pair of ordinary differential an infinite order as well as an algebraic been obtained and solved by a power series of a parameter which depends upon the the Froude number.last two problems, and by the aid of the water theory, a nonlinear perturbation method is develop a solution for the case of an obstacle of shape, then the results are computed for the case of gentle slope.
hree problems, the computed results have been ed and discussed.