On the integrability of nonlinear Dirac equations

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Abstract
The integrability of nonlinear Dirac equations is discussed applying recent results in soliton theory. Using the Lie point transformation groups of the nonlinear Dirac equations we reduce these partial differential equations to systems of ordinary differential equations and study whether these systems are integrable. We also discuss whether Lie–Bäcklund vector fields exist. We conclude that the nonlinear Dirac equations are not integrable.