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Wave Excitation in a Dissipative Medium with a Double Quadratically-Modular Nonlinearity: a Generalization of the Inhomogeneous Burgers Equation

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Abstract

Solutions of a forced (inhomogeneous) partial differential equation of the second order with two types of nonlinearity: power (quadratic) and nonanalytic (modular) are found. Equations containing each of these nonlinearities separately were studied earlier. A natural continuation of these studies is the development of the theory of wave phenomena in a medium with a double nonlinearity, which have recently been observed in experiments. Here solutions describing the profiles of intense waves are derived. Shapes of freely propagating stationary perturbations in the form of shock waves with a finite front width are found. The profiles of forced waves excited by external sources are calculated.

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Authors and Affiliations

  1. Physics Faculty, Moscow State University, Moscow, 119991, Russia

    O. V. Rudenko

  2. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia

    O. V. Rudenko

  3. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia

    O. V. Rudenko

  4. Blekinge Institute of Technology, Karlskrona, Sweden

    O. V. Rudenko

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  1. O. V. Rudenko
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Correspondence to O. V. Rudenko.

Additional information

Published in Russian in Doklady Akademii Nauk, 2018, Vol. 480, No. 3, pp. 273–277.

The article was translated by the author.

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Rudenko, O.V. Wave Excitation in a Dissipative Medium with a Double Quadratically-Modular Nonlinearity: a Generalization of the Inhomogeneous Burgers Equation. Dokl. Math. 97, 279–282 (2018). https://doi.org/10.1134/S1064562418030110

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  • DOI: https://doi.org/10.1134/S1064562418030110

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