  The class of static solutions found by Gibbons and Wells for
dilaton-electrodynamics in flat spacetime, which describe nontopological
strings and walls that trap magnetic flux, is extended to a class of dynamical
solutions supporting arbitrarily large, nondissipative traveling waves, using
techniques previously applied to global and local topological defects. These
solutions can then be used in conjunction with S-duality to obtain more general
solitonic solutions for various axidilaton-Maxwell theories. As an example, a
set of dynamical solutions is found for axion, dilaton, and Maxwell fields in
low energy heterotic string theory using the SL(2,R) invariance of the
equations of motion.
