  We determine conditions under which a generic gauge invariant nonautonomous
and inhomogeneous nonlinear partial differential equation in the
two-dimensional space-time continuum can be transform into standard autonomous
forms. In addition to the nonlinear Schroedinger equation, important examples
include the derivative nonlinear Schroedinger equation, the quintic complex
Ginzburg-Landau equation, and the Gerdjikov-Ivanov equation. This approach
provides a mathematical description of nonstationary media supporting
unidimensional signal propagation and/or total field trapping. In particular,
we study self-similar and nonspreading wave packets for Schroedinger equations.
Some other important coherent structures are also analyzed and applications to
nonlinear waves in inhomogeneous media such as atmospheric plasma, fiber
optics, hydrodynamics, and Bose-Einstein condensation are discussed.
