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IMA Journal of Applied Mathematics 1978 21(1):25-40; doi:10.1093/imamat/21.1.25
© 1978 by Institute of Mathematics and its Applications
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Wave Propagation in Dissipative or Dispersive Non-linear Media

M. TEYMUR and E. SUHUBI

Applied Mathematics Division, Marmara Scientific and Industrial Research Institute P.K.141 Kadikdy-Istanbul, Turkey
Applied Mathematics Division, Marmara Scientific and Industrial Research Institute and Department of Theoretical Mechanics, Faculty of Sciences, Technical University of Istanbul Turkey

A singular perturbation method is developed to investigate one dimensional weak nonlinear waves in dissipative or dispersive media. Utilizing this method a boundary value problem for a system of partial differential equations characterizing wave propagation in homogeneous dissipative or dispersive media is studied. In order to obtain a first-order uniformly valid solution, the problem is reduced to an initial value problem for scalar non-linear partial differential equation. Some special cases arising from the structure of coefficient matrices are examined and the method is extended to these cases. As an application of the perturbation method, various problems of wave propagation in a finite linear viscoelastic half-space are studied.


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