Geodesic
Nonlinear longitudinal waves in inhomogeneous rods
Zapiski Nauchnykh Seminarov POMI, Interference waves in layered media. Part I, Tome 99 (1980), pp. 64-73

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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. 
@article{ZNSL_1980_99_a6,
     author = {I. A. Molotkov and S. A. Vakulenko},
     title = {Nonlinear longitudinal waves in inhomogeneous rods},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {64--73},
     publisher = {mathdoc},
     volume = {99},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1980_99_a6/}
}
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I. A. Molotkov; S. A. Vakulenko. Nonlinear longitudinal waves in inhomogeneous rods. Zapiski Nauchnykh Seminarov POMI, Interference waves in layered media. Part I, Tome 99 (1980), pp. 64-73. http://geodesic.mathdoc.fr/item/ZNSL_1980_99_a6/