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.
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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).
V. I. Fushchich, “On symmetries and exact solutions of higher-dimensional nonlinear wave equations,” Ukr. Mat. Zh.,39, No. 1, 116–123 (1987).
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).
V. I. Fushchich and R. Z. Zhdanov, “Symmetry and exact solutions of nonlinear spinor equations,” Phys. Rep.,174, No. 4, 123–174 (1989).
L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 958–962, July, 1990.
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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
- Differential Equation
- Exact Solution
- Ordinary Differential Equation
- Arbitrary Function
- Dirac Equation