Abstract
This thesis consists of two largely independent parts. Part I is again divided into sub-division A and sub-division B. In sub-division A the problem of solitary waves under the influence of gravity and surface tension has been considered. It has been shown that in the presence of surface tension super-critical flow of the fluid corresponds to waves of elevation only, whereas sub-critical flow corresponds to waves of depression only. The equation of the free surface and the expressions for the velocity components of the fluid particles have been derived in each case. Sub-division B is a discussion of the effects of surface tension on an advancing solitary wave of finite steepness. It has been found that as in the case of periodic waves an advancing gravitational solitary wave also produces a train of short capillary waves on its forward face. In part II we have solved the problem of capillary-gravity waves on a sloping beach. Two different classes of solutions have been obtained by slightly different methods. The first method which is applicable for all values of the slope angles alpha< pi/2 gives rise to a class of solutions which we call the first class of solutions. The second method gives rise to a second class of solutions and this method works only when the slope angle is of the form pi/2n with n an integer. Both classes of solutions behave at infinity like simple harmonic progressive waves, whereas at the shore line the first class of solutions have algebraic singularities and the second class of solutions remain, in general, bounded, but for the special case pi - 2beta = 2qalpha (alpha < pi/8 , q an integer and beta a constant specified later) the second class of solutions have logarithmic singularities at the shore line.