On one equation of internal waves

The Cauchy-Dirichlet problem is considered for the equation of internal waves. This equation has various applications in hydrodynamics, for example, in the study of waves in the ocean. The article provides an analytical study of one equation of internal waves. This equation characterizes propagation of waves in a homogeneous incompressible stratified fluid. The equation of internal waves is reduced to an abstract semilinear Sobolev type equation of the second order. The study of the equation is carried out within the framework of the theory of polynomially bounded operator pencils. In this work, we construct propagators for the equation of internal waves. Also, we present two model examples, where the domain D is represented in the form of a cylinder and a parallelepiped. The result of the work is an analytical solution to the considered cases for the equation of internal waves.