Article

Ricerche di Matematica

, Volume 56, Issue 1, pp 19-30

First online:

The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation

  • Shuji MachiharaAffiliated withShimane University, Department of Mathematics, Matsue 690-8504
  • , Takayuki OmosoAffiliated withShimane University, Department of Mathematics, Matsue 690-8504

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Abstract

In [3] Dias and Figueira have reported that the square of the solution for the nonlinear Dirac equation satisfies the linear wave equation in one space dimension. So the aim of this paper is to proceed with their work and to clarify a structure of the nonlinear Dirac equation. The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation are obtained.

Keywords: Nonlinear Dirac equation, Dirac-Klein-Gordon equation, Pauli matrix

Mathematics Subject Classification (2000): 35C05, 35L45