Summary
The range of validity of a simple wave approximation to a non-linear set of two dissipative wave equations has been studied. The non-linear set is, when the dissipative terms are omitted, totally exceptional. It describes the propagation of longitudinal waves in an ideal elastic bar with some viscous stress. Upon a non-linear transformation, the equations become linear. These linear equations have been studied first. The results for the non-linear equations are then easily obtained by transforming backwards. It turns out that, if the non-linearity is small enough, they are similar to those obtained for the linear equations.
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Broer, L.J.F., Schuurmans, M.F.H. On a simple wave approximation to a non-linear problem. J Eng Math 5, 109–120 (1971). https://doi.org/10.1007/BF01535402
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DOI: https://doi.org/10.1007/BF01535402