Order preserving vibrating strings and applications to electrodynamics and magnetohydrodynamics

The motion of a collection of vertical strings subject to horizontal linear vibrations in the plane can be described by a system of first order nonlinear conservations laws. This system -that we call the Chaplygin-Born-Infeld (CBI) system-is related to Magnetohydrodynamics and more specifically to its shallow water version. Then, each vibrating string can be interpreted as a magnetic line. The CBI system is also related to the Born-Infeld theory for the electromagnetic field, a nonlinear correction to the classical Maxwell's equations.