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Destruction of a Singularity of a Strongly Nonlinear Wave Profile in a Dissipative Medium

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Abstract

Explanations of the term “strongly nonlinear wave” are given, and a possible classification of the corresponding mathematical models is described. The parameters are discussed for which it is reasonable to call the mechanical and electromagnetic waves “strong” and distinguish them from weakly nonlinear waves, the nonlinear effects in which can also be strongly expressed. Exact “stationary” solutions with singularities are studied in the example of evolution equations with quadratic and modular nonlinearities. It is shown that these solutions in fact are not stationary, since the singularities arising in them are rapidly destroyed due to the manifestation of nonlinear and dissipative properties of the medium.

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REFERENCES

  1. O. V. Rudenko and C. M. Hedberg, Acoust. Phys. 59 (6), 644 (2013).

    Article  ADS  Google Scholar 

  2. O. V. Rudenko, S. N. Gurbatov, and C. M. Hedberg, Nonlinear Acoustics through Problems and Examples (Fizmatlit, M., 2007; Trafford, Victoria BC, Canada, 2011).

  3. E. Pelinovsky, Hydrodynamics of Tsunami Waves, in: Waves in Geophysical Fluids (Springer, Vienna, 2006).

    Google Scholar 

  4. E. A. Khazanov and A. M. Sergeev, Phys.-Usp. 51 (4), 969 (2008).

    Article  Google Scholar 

  5. S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics (Gordon and Breach, NY, 1972).

    Google Scholar 

  6. O. V. Rudenko, Applied Nonlinear Dynamics 26 (3), 7 (2018). https://doi.org/10.18500/0869-6632-2018-26-3-7-34

    Google Scholar 

  7. W. Heisenberg, Nachr. Acad. Wiss. Goettingen IIa (8), 111 (1953).

  8. A. B. Prudnikov, Yu. A. Brychkov, and, O. I. Marichev, Integrals and Series: Elementary Functions (Nauka, M., 1981; CRC Press, NY, 1992).

  9. O. V. Rudenko and S. I. Soluyan, Dokl. Akad. Nauk SSSR 190 (4), 815 (1970).

    Google Scholar 

  10. A. D. Polyanin, A. V. Vyaz’min, A. I. Zhurov, and D. A. Kazenin, Handbook of Nonlinear Partial Differential Equations (Chapman & Hall/CRC Press, Boca Raton, 2012).

    Google Scholar 

  11. O. V. Rudenko and V. A. Gusev, Dokl. Math. 93 (1), 94 (2016).

    Article  MathSciNet  Google Scholar 

  12. N. N. Nefedov and O. V. Rudenko, Dokl. Math. 97 (1), 99 (2018).

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported by the Russian Science Foundation, grant no. 19-12-00098.

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Authors and Affiliations

  1. Moscow State University, 119991, Moscow, Russia

    O. V. Rudenko

  2. Prokhorov Institute of General Physics, Russian Academy of Sciences, 117942, Moscow, Russia

    O. V. Rudenko

  3. Schmidt Joint Institute of Physics of the Earth, Russian Academy of Sciences, 123242, Moscow, Russia

    O. V. Rudenko

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

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Rudenko, O.V. Destruction of a Singularity of a Strongly Nonlinear Wave Profile in a Dissipative Medium. Dokl. Phys. 65, 169–173 (2020). https://doi.org/10.1134/S1028335820050092

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  • DOI: https://doi.org/10.1134/S1028335820050092

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