Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Non-Lie ansatzen and exact solutions of a nonlinear spinor equation

  • 23 Accesses

  • 2 Citations

Abstract

Using the conditional symmetry of the nonlinear Dirac equation new ansatzen are obtained for a spinor field which reduce this equation to ordinary differential equations. A new class of exact solutions of the nonlinear Dirac equation, which contains three arbitrary functions, is constructed.

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

Literature cited

  1. 1.

    V. I. Fushchich, “How to extend the symmetry of differential equations,” in: Symmetry and Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Institute of Mathematics, Kiev, Akad. Nauk UkrSSR, 4–16 (1987).

  2. 2.

    V. I. Fushchich, “On symmetries and exact solutions of higher-dimensional nonlinear wave equations,” Ukr. Mat. Zh.,39, No. 1, 116–123 (1987).

  3. 3.

    V. I. Fushchich and I. M. Tsifra, “On a reduction on solutions of nonlinear wave equations with broken symmetry,” J. Phys., A,20, No. 2, L45-L48 (1987).

  4. 4.

    V. I. Fushchich and R. Z. Zhdanov, “Symmetry and exact solutions of nonlinear spinor equations,” Phys. Rep.,174, No. 4, 123–174 (1989).

  5. 5.

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

Download references

Author information

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 958–962, July, 1990.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Fushchich, V.I., Zhdanov, R.Z. Non-Lie ansatzen and exact solutions of a nonlinear spinor equation. Ukr Math J 42, 851–855 (1990). https://doi.org/10.1007/BF01062090

Download citation

Keywords

  • Differential Equation
  • Exact Solution
  • Ordinary Differential Equation
  • Arbitrary Function
  • Dirac Equation