Skip to main content
SpringerLink
Log in

Nonlinear d'alembert equation in the pseudo-euclidean spaceR 2,n and its solutions

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We investigate the nonlinear D'Alembert equation in the pseudo-Euclidean spaceR 2,n and construct new exact solutions containing arbitrary functions.

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, V. M. Shtelen', and N. I. Serov,Symmetric Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

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

    Google Scholar 

  3. V. I. Fushchich, A. F. Barannik, and Yu. D. Moskalenko, “On exact solutions of nonlinear D'Alembert and Liouville equations in the pseudo-Euclidean spaceR 2.2. I,”Ukr. Mat. Zh.,42, No. 8, 1122–1128 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  4. V. I. Fushchich, A. F. Barannik, and Yu. D. Moskalenko, “On exact solutions of nonlinear D'Alembert and Liouville equations in the pseudo-Euclidean spaceR 2,2. II,”Ukr. Mat. Zh.,42, No. 9, 1237–1244 (1990).

    MathSciNet  Google Scholar 

  5. A. F. Barannik and Yu. D. Moskalenko, “On the reduction of an ultrahyperbolic D'Alembert equation in the pseudo-Euclidean spaceR 2,2,”Dokl. Akad. Nauk Ukr. SSR, No. 9, 3–6 (1990).

    MathSciNet  Google Scholar 

  6. A. F. Barannik and I. I. Yuryk, “On a new method for constructing exact solutions of the nonlinear differential equations of mathematical physics,”J. Phys. A: Math. Gen.,31, L4899-L4907 (1998).

    Article  MathSciNet  Google Scholar 

  7. A. F. Barannik and I. I. Yuryk, “A new method for the construction of solutions of nonlinear wave equations,”Ukr. Mat. Zh.,51, No. 5, 583–593 (1999).

    MATH  Google Scholar 

  8. V. I. Smirnov and S. L. Sobolev, “A new method for the solution of the plane problem of elastic vibrations,”Tr. Seism. Inst. AN SSSR, No. 20, 1–37 (1932).

    Google Scholar 

  9. V. I. Smirnov and S. L. Sobolev, “On the application of a new method to the investigation of oscillations in space in the presence of axial symmetry,”Tr. Seism. Inst. AN SSSR, No. 29, 43–51 (1933).

    Google Scholar 

  10. V. I. Fushchich, R. Z. Zhdanov, and I. V. Revenko, “General solution of a nonlinear wave equation and an eikonal equation,”Ukr. Mat. Zh.,43, No. 11, 1471–1486 (1991).

    MathSciNet  Google Scholar 

Download references

Authors
  1. I. I. Yuryk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Ukrainian University of Food Technology, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 820–827, June, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yuryk, I.I. Nonlinear d'alembert equation in the pseudo-euclidean spaceR 2,n and its solutions. Ukr Math J 52, 940–949 (2000). https://doi.org/10.1007/BF02591787

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02591787

Keywords

Search

Navigation