We review the proof of existence and uniqueness of solutions of the Maxwell-Schrödinger system in a neighborhood of infinity in time, with prescribed asymptotic behaviour defined in terms of asymptotic data, without any restriction on the size of those data. That result is the basic step in the construction of modified wave operators for the Maxwell-Schrödinger system.
"Long range scattering for the Maxwell-Schrödinger system with arbitrarily large asymptotic data." Hokkaido Math. J. 37 (4) 795 - 811, November 2008. https://doi.org/10.14492/hokmj/1249046369