Solitons in an extended nonlinear Schr\"odinger equation with   third-order dispersion and pseudo-Raman effect
  Dynamics of solitons is considered in an extended nonlinear Schr\"odinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, third-order dispersion (TOD) and inhomogeneity of the spatial second-order dispersion (SOD). It is shown that wave-number downshift by the pseudo-SRS may be compensated by upshift provided by spatially increasing SOD with taking into account TOD. The equilibrium state is stable for positive parameter of TOD and unstable for negative one. The analytical solutions are verified by comparison with numerical results 
A.V. Aseeva, L.G. Blyakhman, E.M. Gromov, V.V. Tyutin
nlin.PS