We extend the classical integrability of the CGHS model of 2d dilaton gravity
[1] to a larger class of models, allowing the gravitational part of the action
to depend more generally on the dilaton field and, simultaneously, adding
fermion- and U(1)-gauge-fields to the scalar matter. On the other hand we
provide the complete solution of the most general dilaton-dependent 2d gravity
action coupled to chiral fermions. The latter analysis is generalized to a
chiral fermion multiplet with a non-abelian gauge symmetry as well as to the
(anti-)self-dual sector df = *df (df = -*df) of a scalar field f.Comment: 37 pages, Latex; typos and Eqs. (44,45) corrected; paragraph on p.
26, referring to a work of S. Solodukhin, reformulated; references adde
