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Effect of Defects on the Spatial Localization of Nonlinear Acoustic Waves

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Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

A self-consistent mathematical model that includes equations of elasticity theory and kinetic equations for the density of different types of point defects is reduced to a nonlinear equation of evolution that combines the familiar Korteweg–de Vries–Burgers and Klein–Gordon equations of wave dynamics. Exact analytical solutions for this equation are found and analyzed.

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References

  1. Mirzoev, F.Kh., Panchenko, V.Ya., and Shelepin, L.A., Phys.-Usp., 1996, vol. 39, p.1.

    Article  ADS  Google Scholar 

  2. Burlak, G.N. and Ostrovskii, I.V., Tech. Phys. Lett., 1997, vol. 23, no. 9, p.725.

    Article  ADS  Google Scholar 

  3. Erofeev, V.I. and Romashov, V.P., Tech. Phys. Lett., 2002, vol. 28, no. 3, p.218.

    Article  ADS  Google Scholar 

  4. Erofeev, V.I. and Romashov, V.P., Russ. J. Nondestr. Test., 2004, vol. 40, no. 1, p.46.

    Article  Google Scholar 

  5. Erofeev, V.I., Tech. Phys. Lett., 2008, vol. 34, no. 2, p.150.

    Article  ADS  Google Scholar 

  6. Bagdoev, A.G., Erofeyev, V.I., and Shekoyan, A.V., Lineinye i nelineinye volny v dispergiruyushchikh sploshnykh sredakh (Wave Dynamics of Generalized Continua), Moscow: Fizmatlit, 2009.

    Google Scholar 

  7. Shekoyan, A.V., Tech. Phys. Lett., 2009, vol. 35, no. 4, p.337.

    Article  MathSciNet  ADS  Google Scholar 

  8. Erofeev, V.I. and Kazhaev, V.V., Tech. Phys., 2010, vol. 55, no. 4, p.580.

    Article  Google Scholar 

  9. Sarafanov, G.F., Kollektivnye i volnovye effekty v ansamble dislokatsii pri plasticheskoi deformatsii metallov (Collective and Wave Effects in a Dislocation Ensemble in the Process of Plastic Deformation of Metals), Nizhny Novgorod: Litera, 2010.

    Google Scholar 

  10. Erofeev, V.I. and Mal’khanov, A.O., Fiz. Mezomekh., 2017, vol. 20, no. 4, p.69.

    Google Scholar 

  11. Erofeev, V.I. and Malkhanov, A.O., Procedia IUTAM, 2017, vol. 23, p.228.

    Article  Google Scholar 

  12. Mirzoev, F.Kh. and Shelepin, L.A., Tech. Phys., 2001, vol. 46, no. 8, p.952.

    Article  Google Scholar 

  13. Kudryashov, N.A., Analiticheskaya teoriya nelineinykh differentsial’nykh uravnenii (Analytical Theory of Nonlinear Differential Equations), Moscow–Izhevsk: Inst. Komp’yut. Issled., 2004.

    Google Scholar 

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Correspondence to V. I. Erofeev.

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Original Russian Text © V.I. Erofeev, A.V. Leonteva, A.O. Malhanov, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Seriya Fizicheskaya, 2018, Vol. 82, No. 5.

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Erofeev, V.I., Leonteva, A.V. & Malhanov, A.O. Effect of Defects on the Spatial Localization of Nonlinear Acoustic Waves. Bull. Russ. Acad. Sci. Phys. 82, 520–525 (2018). https://doi.org/10.3103/S1062873818050088

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  • DOI: https://doi.org/10.3103/S1062873818050088

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