Abstract
Substitutions are proposed, reducing a system of nonlinear Dirac equations to ordinary differential equations, integrable in special functions. It is established that the class of special functions in which the solution of the Dirac equation is written essentially depends on the form of nonlinearity.
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Literature cited
W. I. Fushchich and R. Z. Zhdanov, “On some exact solutions of a system of nonlinear differential equations for spinor and vector fields,” J. Phys. A: Math. and Gen.,20, No. 13, 4173–4190 (1987).
E. Kamke, Handbook of Ordinary Differential Equations [in Russian], Nauka, Moscow (1976).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 564–568, April, 1990.
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Zhdanov, R.Z., Revenko, I.V. Exact solutions of the nonlinear Dirac equation in terms of Bessel, Gauss and Legendre functions and Chebyshev-Hermite polynomials. Ukr Math J 42, 500–503 (1990). https://doi.org/10.1007/BF01071344
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DOI: https://doi.org/10.1007/BF01071344