Skip to main content
SpringerLink
Log in

Galilei-invariant higher-order equations of burgers and korteweg-de vries types

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We describe nonlinear Galilei-invariant higher-order equations of Burgers and Korteweg-de Vries types. We study symmetry properties of these equations and construct new nonlinear extensions for the Galilei algebra AG(1, 1).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. B. Whitham,Linear and Nonlinear Waves, Wiley, New York 1974.

    MATH  Google Scholar 

  2. V. A. Krasil’nikov and V. A. Krylov,Introduction to Physical Acoustics [in Russian], Nauka, Moscow 1984.

    Google Scholar 

  3. O. V. Rudenko and S. I. Soluyan,Theoretical Foundations of Nonlinear Acoustics [in Russian], Nauka, Moscow 1975.

    Google Scholar 

  4. P. L. Sachdev,Nonlinear Diffusive Waves, Cambridge University Press, Cambridge 1987.

    MATH  Google Scholar 

  5. W. I. Fushchych, W. Shtelen, and N. Serov,Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics, Kluwer, Dordrecht 1993.

    Google Scholar 

  6. P. J. Olver,Applications of Lie Groups to Differential Equations, Springer, New York 1986.

    MATH  Google Scholar 

  7. W. I. Fushchych and P. I. Myronyuk, “Conditional symmetry and exact solutions of equations of nonlinear acoustics,”Dopov. Akad Nauk Ukr., No. 6, 23–39 (1991).

    Google Scholar 

  8. N. I. Serov and B. W. Fushchych, “On a new nonlinear equation with unique symmetry,”Dopov. Akad. Nauk Ukr., No. 9, 49–50 (1994).

    Google Scholar 

  9. P. N. Sionoid and A. T. Cates, “The generalized Bürgers and Zabolotskaya-Khokhlov equations: transformations, exact solutions and qualitative properties,”Proc. Royal Soc.,447, No. 1930, 253–270 (1994).

    Article  MATH  Google Scholar 

  10. W. I. Fushchych, “A new nonlinear equation for electromagnetic fields having velocity different from c,”Dopov. Akad. Nauk Ukr., No. 1, 24–27(1992).

  11. W. I. Fushchych, “Symmetry analysis,” in:Symmetry Analysis of Equations of Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 5–6.

    Google Scholar 

  12. W. I. Fushchych and V. M. Boyko,Symmetry Classification of the One-Dimensional Second Order Equation of Hydrodynamical Type, Preprint LiTH-MATH-R-95-19, Linköping University, Sweden (1995).

    Google Scholar 

  13. V. M. Boyko, “Symmetry classification of the one-dimensional second order equation of a hydrodynamical type,”J. Nonlin. Math. Phys.,2, No. 3–4, 418–424 (1995).

    Article  MathSciNet  Google Scholar 

  14. V. I. Fushchych and V. M. Boiko, “Reduction of order and general solutions for some classes of equations of mathematical physics,”Dopov. Akad. Nauk Ukr., No. 9, 43–48 (1996).

    Google Scholar 

Download references

Authors
  1. W. I. Fushchych
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. M. Boiko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fushchych, W.I., Boiko, V.M. Galilei-invariant higher-order equations of burgers and korteweg-de vries types. Ukr Math J 48, 1799–1814 (1996). https://doi.org/10.1007/BF02375368

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02375368

Keywords

Search

Navigation