Nonlinear singular integral equations in elastodynamics by using Hilbert transformations

A seismic wave equations analysis is investigated by reducing the problem to the solution of a nonlinear singular integral equation. Therefore, the solution of the seismic wave equation, which is of great importance in the theory of elastodynamics, by using Hilbert transformations is reduced to such a type of singular integral equation. Some approximate solutions, are finally constructed by using Hilbert transform operators for the solution of the nonlinear singular integral equations.