Nonlinear longitudinal waves in inhomogeneous rods

The equation for longitudinal waves in bars taking into account of a nonlinearity, dispersion and inhomogeneity is obtained. This equation is the perturbed equation of Korteweg–de Vries. A perturbance method for solution of Cauchy problems for this equation is found. The obtained solution describes the soliton deformation under the influence of the bar inhomogeneity.