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

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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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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).

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

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    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).

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

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

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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).

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