Exact solutions of the nonlinear Dirac equation in terms of Bessel, Gauss and Legendre functions and Chebyshev-Hermite polynomials

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.