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Einstein's relation E=Mc^2 between the energy E and the mass M is thecornerstone of the relativity theory. This relation is often derived in acontext of the relativistic theory for closed systems which do not accelerate.By contrast, Newtonian approach to the mass is based on an accelerated motion.We study here a particular neoclassical field model of a particle governed by anonlinear Klein-Gordon (KG) field equation. We prove that if a solution to thenonlinear KG equation and its energy density concentrate at a trajectory, thenthis trajectory and the energy must satisfy the relativistic version ofNewton's law with the mass satisfying Einstein's relation. Therefore theinternal energy of a localized wave affects its acceleration in an externalfield as the inertial mass does in Newtonian mechanics. We demonstrate that the"concentration" assumptions hold for a wide class of rectilinear acceleratingmotions.

Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation