Propagation of an envelope soliton in a medium with spatially varying dispersion

We study analytically and numerically the motion of a nonlinear Schrodinger soliton in a medium with spatially modulated dispersion. The cases of periodic and random modulations of the dispersive term are considered. In the former, numerical simulations for small velocities show a good agreement with the adiabatic equations. When the velocity is increased the soliton emits linear waves and we calculate their spectral density and show the existence of a resonant condition connecting the amplitude and velocity of the soliton to the wavelength of the modulation. The important application of steering a spatial soliton in an array of tunnel coupled planar waveguides with variable coupling is considered.