Analytical solutions of the equation describing internal gravity waves generated by a moving nonlocal source of perturbations

The problem of constructing analytical solutions describing internal gravity wave fields generated by a nonlocal source of perturbations moving on the surface of a stratified medium of finite depth is considered. For a radially symmetric model source, analytical solutions expressed in terms of eigenfunctions of the basic vertical spectral problem for internal waves are obtained in the linear approximation. Two methods of solution representation, including one based on the Mittag-Leffler theorem on expansion of a meromorphic function, are proposed. Numerically computed wave fields for various modes of wave generation are presented, which illustrate two methods of analytical wave field representation.