  Applying the method of characteristics leads to wavefunctions and dynamic
localization conditions for electrons on the one dimensional lattice under
perpendicular time dependent electric and magnetic fields. Such conditions
proceed again in terms of sums of products of Bessel functions of the first
kind. However, this time one deals with both the number of magnetic flux quanta
times $\pi $ and the quotients between the Bloch frequency and the ones
characterizing competing fields. Tuning the phases of time dependent
modulations leads to interesting frequency mixing effects providing an
appreciable simplification of dynamic localization conditions one looks for.
The understanding is that proceeding in this manner, the time dependent
superposition mentioned above gets reduced effectively to the influence of
individual ac-fields exhibiting mixed frequency quotients. Besides pure field
limits and superpositions between uniform electric and time dependent magnetic
fields, parity and periodicity effects have also been discussed.
