Skip to main content
SpringerLink
Log in

Exact solutions of the d'alembert and liouville equations in the pseudo-Euclidean space R2, 2· I

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

A description is obtained of the rank-2 and rank-3 maximal subalgebras of the extended Poincare algebra AP(2,2), which is the maximal invariance algebra of the equation □u+F(u)=0, where F(u)=λuk, k ≠ 1 or F(u)= λexp u.

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

Literature cited

  1. V. I. Fushchich, V. M. Shtelen', and N. I. Serov, Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  2. L. F. Barannik and V. I. Fushchich, “On continuous subgroups of the pseudo-orthogonal and pseudo-unitary groups,” Preprint, No. 86.87, Inst. Mat., Akad. Nauk Ukr. SSR (1986).

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

    Google Scholar 

  4. L. F. Barannik, “Symmetry reduction and exact solutions of the Liouville equation,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 3–5 (1988).

    Google Scholar 

  5. V. I. Fushchich, “Symmetry in problems of mathematical physics,” in: Algebraic-Theoretic Methods of Investigation in Mathematical Physics [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1981), pp. 6–28.

    Google Scholar 

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

    Google Scholar 

  7. L. F. Barannik, V. I. Lagno, and V. I. Fushchich, “Subalgebras of the Poincare algebra AP(2, 3) and symmetry reduction of the nonlinear ultrahyperbolic d'Alembert equation. I.,” Ukr. Mat. Zh.,40, No. 4, 411–416 (1988).

    Google Scholar 

  8. L. F. Barannik, V. I. Lagno, and V. I. Fushchich, “Subalgebras of the Poincare algebra AP(2, 3) and symmetry reduction of the nonlinear ultrahyperbolic d'Alembert equation, II,” Ukr. Mat. Zh.,41, No. 5, 579–584 (1989).

    Google Scholar 

  9. L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  10. J. Patera, P. Winternitz, and H. Zassenhaus, “Continuous subgroups of the fundamental groups of physics. II. The similitude group,” J. Math. Phys.,16, No. 8, 1615–1624 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Institute, Academy of Sciences of the Ukrainian SSR, Kiev

    V. I. Fushchich, A. F. Barannik & Yu. D. Moskalenko

Authors
  1. V. I. Fushchich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. F. Barannik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu. D. Moskalenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1122–1128, August, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fushchich, V.I., Barannik, A.F. & Moskalenko, Y.D. Exact solutions of the d'alembert and liouville equations in the pseudo-Euclidean space R2, 2· I. Ukr Math J 42, 1001–1006 (1990). https://doi.org/10.1007/BF01099234

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01099234

Keywords

Search

Navigation