The General and Asymptotic Solution of the Elastic Wave Equation in an Unbounded Medium

New forms and new properties are given for the general solution of the three-dimensional dynamic equation for the displacement vector in an isotropic linear elastic solid. The general initial value problem in an unbounded medium with no sources is solved. The general solution at an arbitrary time is given in terms of two asymptotic vector fields. One is thereby able to obtain the complete and exact solution, including initial conditions, which corresponds to a specified or desired asymptotic solution, valid for large times in the future. The complete elastic field energy of an arbitrary exact solution is also shown to depend, in a simple way, only on the two asymptotic vector fields.