Asymptotic solution of equations of motion for a longitudinal wave propagating in a nonlinear elastic homogeneous medium is sought. The solution consists of the basic term known from the solution of linear problems, and from two corrections caused by nonlinearity of the medium. Nonlinearity leads to several interesting phenomena unknown in linear media. Examples are appearance of a wave with doubled frequency with respect to the basic mode, or appearance of transverse component of the displacement vector of the longitudinal wave propagating in a homogeneous medium.
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