Nonlinear wave and soliton propagation in media with arbitrary inhomogeneities

Asymptotic solutions of nonlinear wave propagation in media with gentle, but otherwise arbitrary density inhomogeneities, are discussed. In the adiabatic approximation, a nonlinear Schroedinger equation is derived for media with linear, but time-dependent density gradients. The resulting extra term can be eliminated by going to an accelerated reference frame, which makes this modified nonlinear Schroedinger equation completely integrable by the inverse scattering method. Multi-solitons are therefore still the asymptotic states of waves propagating in media with arbitrary inhomogeneities