Physics of Particles and Nuclei Letters

, Volume 8, Issue 4, pp 395–398 | Cite as

Numerical and analytical study of wave processes in periodic stratified media

  • S. I. Serdyukova
Computer Technologies in Physics


We study the behaviour of the solutions of the Cauchy problem with discontinuous initial data for nonstandard linear partial differential equations modeling wave processes in periodic stratified media. Asymptotic formulas at large t are derived. The found asymptotic formulas are in a good agreement with the results of numerical experiments done by using the analytical computation system REDUCE 3.8.


Cauchy Problem Asymptotic Formula Nucleus Letter Wave Process Oscillation Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. S. Bakhvalov and M. E. Eglit, “Effective Equations with Dispersion for Wave Propagation in Periodic Media,” Dokl. Akad. Nauk 370 7–10 (2000) [Dokl. Math. 61, 1–4 (2000)].MathSciNetGoogle Scholar
  2. 2.
    N. S. Bakhvalov and M. E. Eglit, “Study of Effective Equations with Dispersion for Wave Propagation in Stratified Media and Thin Plates,” Dokl. Akad. Nauk 383, 742–746 (2002) [Dokl. Math. 65, 301–305 (2002)].MathSciNetGoogle Scholar
  3. 3.
    N. S. Bakhvalov and G. P. Panasenko, Averaging Processes in Periodic Media (Nauka, Moscow, 1984) [in Russian].MATHGoogle Scholar
  4. 4.
    S. I. Serdyukova, “Exotic Asymptotics for a Linear Hyperbolic Equation,” Dokl. Akad. Nauk 389, 305–309 (2003) [Dokl. Math. 67, 203–207 (2003)].MathSciNetGoogle Scholar
  5. 5.
    REDUCE User’s Guide for Unix Systems, Version 3.8 by Winfried Neun, ZiB D-14195 (Dahlem, Berlin, 2004).Google Scholar
  6. 6.
    V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1988), p. 79 [in Russian].MATHGoogle Scholar
  7. 7.
    I. G. Petrovskii, “On the Cauchy Problem for Linear Partial Differential Equations Systems in Domain of Non-Analytical Functions,” Bull. Moscow State Univ. A, No. 1 (1938).Google Scholar
  8. 8.
    S. I. Serdyukova, “Hard Transition from a Stationary State to Oscillations for a Linear Differential Equation,” Dokl. Akad. Nauk 415, 310–314 (2007) [Dokl. Math. 76, 554–558 (2007)].MathSciNetGoogle Scholar
  9. 9.
    S. I. Serdyukova, “Deformation of a Breather-Type Solution after Adding a Lower Term with a Complex Coefficient,” Dokl. Akad. Nauk 427, 17–23 (2009) [Dokl. Math. 80, 1–7 (2009)].MathSciNetGoogle Scholar
  10. 10.
    M. V. Fedoryuk, Asymptotics: Integrals and Series (Nauka, Moscow, 1987) [in Russian].MATHGoogle Scholar
  11. 11.
    M. V. Fedoryuk, “Green’s Function Asymptotics as t → +0, x → ∞ inf for Well Posed in the Sense of Petrovskii Equations with Constant Coefficients and Correctness Classes of the Cauchy Problem Solutions,” Mat. Sb. 62(104), 397–486 (1963).MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • S. I. Serdyukova
    • 1
  1. 1.Joint Institute for Nuclear ResearchDubnaRussia

Personalised recommendations