From Maxwell Stresses to Nonlinear Field Equations

Abstract

This paper aims to show that making use of Newton's view on equations of motion of a physical system and of the Maxwell stress tensor we come to a natural nonlinearization of Maxwell equations in vacuum making use only of nonrelativistic terms. The new equations include all Maxwell solutions plus new ones, among which one may find time-stable and spatially finite ones with photon-like properties and behavior.