Simple Solutions to the Linear Problem of the Generation of Long Waves on the Surface of a Liquid by a Source in an Elastic Foundation Bottom

Abstract The problem of wave generation on the surface of a liquid layer lying on an elastic half-space is considered. The generation source is located in an elastic medium. The joint system of equations of the theory of elasticity in a half-space and the theory of waves in a liquid is solved. On the basis of the previously obtained simplified solution of the dispersion equation for the water mode, taking into account the influence of the elastic half-space and the integral representation of the displacement of the liquid surface caused by a source of a simple form, analytical formulas are constructed for solving the problem under the assumption of long waves. Comparison of results obtained by analytical formulas and integral representations is carried out.