The short envelope soliton dynamics in inhomogeneous dispersive media with allowance for stimulated scattering by damped low-frequency waves
We consider the soliton dynamics in terms of the extended nonlinear Schr¨odinger equation taking into account the inhomogeneous linear second-order dispersion (SOD) and stimulated scattering by damped low-frequency waves (SSDW). It is shown that the wave number downshift due to SSDW is compensated by an upshift due to the SOD decrease on the spatial coordinate. A new class of stationary nonlinear localized solutions (solitons) arising as an equilibrium of SSDW and decreasing spatial SOD is found analytically within the framework of the extended inhomogeneous nonlinear Schr¨odinger equation. A regime of the dynamic equilibrium of SSDW and inhomogeneous dispersive medium with the soliton parameters periodically varied in time is found. Analytical and numerical results are in good agreement for this regime.