Solitons in an Extended Nonlinear Schrödinger Equation with Pseudo Stimulated Scattering and Inhomogeneous Cubic Nonlinearity

We consider the soliton dynamics within the framework of an extended nonlinear Schrodinger equation with pseudo stimulated scattering, which occurs from the damped low-frequency waves, and the spatially inhomogeneous cubic nonlinearity. It is shown that the pseudo stimulated scattering, which leads to a shift of the spectrum of the soliton wave numbers to the long-wavelength region, and the nonlinearity, which increases with the coordinate and shifts the soliton spectrum to the short-wavelength region, can be in balance. The soliton solution, which results from this balance, is explicitly obtained.