A Self-Contained Nonlinear Electromagnetic Field Theory: Basic Formulation and Exact Solutions

We develop a self-contained nonlinear electromagnetic theory based on field configurations satisfying E · B ≠ 0. The present model provides a simple nonlinear extension of Maxwell theory in which effective source terms arise self-consistently from the electromagnetic field. We obtain exact stationary solutions for several representative configurations and exact time-dependent solutions illustrating characteristic properties of the nonlinear equations.