  Backlund transformations (BTs) are a useful tool for integrating nonlinear
partial differential equations (PDEs). However, the significance of BTs in
linear problems should not be ignored. In fact, an important linear system of
PDEs in Physics, namely, the Maxwell equations of Electromagnetism, may be
viewed as a BT relating the wave equations for the electric and the magnetic
field, these equations representing integrability conditions for solution of
the Maxwell system. We examine the BT property of this system in detail, both
for the vacuum case and for the case of a linear conducting medium.
