Advertisement

Mathematical Notes

, Volume 104, Issue 5–6, pp 915–921 | Cite as

Exact Step-Like Solutions of One-Dimensional Shallow-Water Equations over a Sloping Bottom

  • A. V. Aksenov
  • S. Yu. Dobrokhotov
  • K. P. Druzhkov
Short Communications
  • 11 Downloads

Keywords

shallow water linearized system of equations exact solution symmetry operator perturbation asymptotics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. J. Stoker, Comm. Pure Appl.Math. 1 (1), 1 (1948).CrossRefGoogle Scholar
  2. 2.
    G. F. Carrier and H. P. Greenspan, J. FluidMech. 4 (1), 97 (1958).CrossRefGoogle Scholar
  3. 3.
    E. N. Pelinovsky and R. Kh. Mazova, Natural Hazards 6 (3), 227 (1992).CrossRefGoogle Scholar
  4. 4.
    S. Yu. Dobrokhotov and B. Tirozzi, Uspekhi Mat. Nauk 65 (1 (391)), 185 (2010) [RussianMath. Surveys 65 (1), 177 (2010)].CrossRefGoogle Scholar
  5. 5.
    Yu. A. Chirkunov, S. Yu. Dobrokhotov, C. B. Medvedev, and D. S. Minenkov, Teoret. Mat. Fiz. 178 (3), 322 (2014) [Theoret. and Math. Phys. 178 (3), 278 (2014)].CrossRefGoogle Scholar
  6. 6.
    A. V. Aksenov and K. P. Druzhkov, Vestnik Nat. Res. Nucl. University “MIFI” 5 (1), 38 (2016).Google Scholar
  7. 7.
    S. Yu. Dobrokhotov and C. Ya. Sekerzh-Zen’kovich, Mat. Zametki 88 (6), 942 (2010) [Math. Notes 88 (6), 894 (2010)].CrossRefGoogle Scholar
  8. 8.
    L. V. Ovsyannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978) [in Russian].zbMATHGoogle Scholar
  9. 9.
    S. Yu. Dobrokhotov, D. S. Minenkov, V. E. Nazaikinskii, and B. Tirozzi, in Theory and Applications in Mathematical Physics (World Sci. Publ., Hackensack, NJ, 2015), pp. 29–47.CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • A. V. Aksenov
    • 1
    • 2
  • S. Yu. Dobrokhotov
    • 3
    • 4
  • K. P. Druzhkov
    • 1
    • 4
  1. 1.LomonosovMoscow State UniversityMoscowRussia
  2. 2.National Research Nuclear University MEPhIMoscowRussia
  3. 3.Ishlinsky Institute for Problems in Mechanics RASMoscowRussia
  4. 4.Moscow Institute of Physics and Technology (State University)DolgoprudnyiRussia

Personalised recommendations