Wave Propagation in Dissipative or Dispersive Non-linear Media

A singular perturbation method is developed to investigate onedimensional weak nonlinear waves in dissipative or dispersivemedia. Utilizing this method a boundary value problem for asystem of partial differential equations characterizing wavepropagation in homogeneous dissipative or dispersive media isstudied. In order to obtain a first-order uniformly valid solution,the problem is reduced to an initial value problem for scalarnon-linear partial differential equation. Some special casesarising from the structure of coefficient matrices are examinedand the method is extended to these cases. As an applicationof the perturbation method, various problems of wave propagationin a finite linear viscoelastic half-space are studied.