Abstract
The work contains two basic results. The first consists in the derivation of an equation for the longitudinal vibrations of a rod which accounts for both nonlinear and dispersion effects as well as effects caused by the inhomogeneity of the material of the rod. This equation is found to be a perturbed Korteweg-de Vries equation. The second result consists in the development of a perturbation method for solving the Cauchy problem for this equation. The solution found describes the deformation of a soliton under the influence of the inhomogeneity of the rod.
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