Particles, 4-vector solitons, and the modified Dirac equations (Q1096807)

If one takes as given that particles are solitons, the nature of those solitons is investigated along with the form of the Dirac equations interpreted as scattering equations. The mathematical structure of 4- vector Bessel functions suggests a 4-vector generalization of the sine- Gordon equation as a possible nonlinear soliton equation. It is also found that the Dirac equations are not suitable as inverse scattering equations as normally given. A set of modified Dirac equations are proposed which replace the point scalar mass with a 4-vector mass-energy potential functions which must satisfy a soliton equation.