Existence of localized solutions for a classical nonlinear Dirac field

• DOI: 10.1007/bf01212340
• Publication Date: 2005-02-25T16:37:45Z
• Authors: Thierry Cazenave; Luis Vazquez
• Keywords: 35Q99; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]; [MATH] Mathematics [math]; [MATH]Mathematics [math]; [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]; 0101 mathematics; 81C05; 01 natural sciences

We prove the existence of stationary states for nonlinear Dirac equations of the form: $$i\gamma ^\mu \partial _\mu \psi - m\psi + F(\bar \psi \psi )\psi = 0.$$ We seek solutions which are separable in spherical coordinates and we use a shooting method for solving the associated problem of ordinary differential equations.