Derivation of Particle, String and Membrane Motions from the Born-infeld Electromagnetism

We derive classical particle, string and membrane motion equations from a rigorous asymptotic analysis of the Born-Infeld nonlinear electromagnetic theory. We first add to the Born-Infeld equations the corresponding energy-momentum conservation laws and write the resulting system as a non-conservative symmetric 10× 10 system of first-order PDEs. Then, we show that four rescaled versions of the system have smooth solutions existing in the (finite) time interval where the corresponding limit problems have smooth solutions. Our analysis is based on a continuation principle previously formulated by the second author for (singular) limit problems.