Skip to main content
SpringerLink
Log in

Reduction of the multidimensional d’Alembert equation to two-dimensional equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We give a classification of maximal subalgebras of rankn−1 for the extended Poincaré algebra\(A\bar P (1.n)\), which is realized on the set of solutions of the d'Alembert equation\(\square u + \lambda u^k = 0\). These subalgebras are used for constructing anzatses that reduce this equation to differential equations with two invariant variables.

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. V. I. Fushchich and N. I. Serov, “The symmetry and some exact solution of the nonlinear many dimensional liouville, d'Alembert, and eikonal equations,”J. Phys. A: Math. Gen.,16, No. 15, 3645–3656 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  2. V. I. Fushchich, V. M. Shtelen', and N. I. Serov,Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics, Kluwer, Dordrecht (1993).

    MATH  Google Scholar 

  3. A. M. Grundland, J. Harnad, and P. Winternitz, “Symmetry reduction for nonlinear relativistic equations,”J. Math. Phys.,25, No. 4, 791–806 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  4. V. I. Fushchich and A. F. Barannik, “Maximal subalgebras of rankn−1 of the algebraA P(1,n) and reduction of nonlinear wave equations. I,”Ukr. Mat. Zh.,42, No. 11, 1552–1559 (1990).

    MathSciNet  Google Scholar 

  5. V. I. Fushchich and A. F. Barannik, “Maximal subalgebras of rankn−1 of the algebraA P(1,n) and reduction of nonlinear wave equations. II,”Ukr. Mat. Zh.,42, No. 12, 1693–1700 (1990).

    MathSciNet  Google Scholar 

  6. V. I. Fushchich, L. F. Barannik, and A. F. Barannik,Subgroup Analysis of Galilei and Poincaré Groups and Reduction of Nonlinear Equations [in Russian], Naukova Dumka, Kiev (1991).

    MATH  Google Scholar 

  7. A. F. Barannik, L. F. Barannik, and V. I. Fushchich, “Reduction of a multidimensional nonlinear Poincaré-invariant equation to two-dimensional equations,”Ukr. Mat. Zh,43, No. 10, 1311–1323 (1991).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pedagogical Institute, Poltava

    A. F. Barannik & L. F. Barannik

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. I. Fushchich

Authors
  1. A. F. Barannik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. F. Barannik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. I. Fushchich
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 651–662, June, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barannik, A.F., Barannik, L.F. & Fushchich, V.I. Reduction of the multidimensional d’Alembert equation to two-dimensional equations. Ukr Math J 46, 699–713 (1994). https://doi.org/10.1007/BF02658172

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02658172

Keywords

Search

Navigation