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Complex phenomena of wave-prestress and wave-material interactions are studied. Model problems of nonlinear propagation of longitudinal waves in materials (i) with inhomogeneous prestress and (ii) with weakly variable physical properties are posed. In both problems two small parameters of different physical nature appear. The problems are solved using the perturbation technique. The influence of the values of two small parameters on the content of terms of perturbative solutions is analysed.doi:10.3176/proc.2010.2.13 fatcat:eo6ptcghsvbh7ejuenk3o7354a