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Nonlinear longitudinal waves in inhomogeneous rods

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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Literature cited

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 99, pp. 64–73, 1980.

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Molotkov, I.A., Vakulenko, S.A. Nonlinear longitudinal waves in inhomogeneous rods. J Math Sci 20, 2434–2441 (1982). https://doi.org/10.1007/BF01087290

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Keywords

  • Soliton
  • Longitudinal Wave
  • Cauchy Problem
  • Perturbation Method
  • Basic Result