Behaviour of the nonlinear Dirac soliton in an external field of the Lorentz scalar type

Abstract

The nonlinear Dirac soliton in an external field of the Lorentz scalar type in (1+1) dimensions is examined by solving the nonlinear Dirac equation numerically. A remarkable feature of the behaviour of the soliton is found, namely, for the linear potential the motion of the soliton centroid is independent of the strength of the nonlinear interaction within the accuracy of the calculation. This feature can be understood by means of a version of the so-called collective variable Ansatz, which leads to an approximate equation of motion for the soliton centroid. It is argued that this feature is characteristic of the case with the linear external potential of the Lorentz scalar type. For the quadratic potential, however, the independence of the motion of the soliton centroid on the strength of the nonlinear interaction is broken very slightly.PACS Nos.: 03.50-w; 03.40.Kf; 11.10.Qr