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Existence of localized solutions for a classical nonlinear Dirac field. (English) Zbl 0596.35117

The paper deals with the existence of stationary states for nonlinear Dirac equations of the form \[ i\sum^{3}_{\mu =0}\gamma^{\mu} \partial_{\mu}\psi -m\psi +F({\bar \psi} \psi)\psi =0 \] under certain hypothesis on F. The notation is the following: \(\psi\) is defined on \(R^ 4\) with values in \(C^ 4\), m is a positive constant, \(\gamma^{\mu}\) are \(4\times 4\) matrices and \({\bar \psi}\) \(\psi\) \(=(\gamma^ 0\psi,\psi)\) where (, ) is the usual scalar product in \(C^ 4.\)
The authors seek solutions which are separable in spherical coordinates and they use a shooting method for solving the associated problem of ordinary differential equations.
Reviewer: Z.Kamont

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35F20 Nonlinear first-order PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
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References:

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