Solitons in a third-order nonlinear Schrödinger equation with the pseudo-Raman scattering and spatially decreasing second-order dispersion

Evolution of solitons is addressed in the framework of a third-order nonlinear Schrödinger equation (NLSE), including nonlinear dispersion, third-order dispersion and a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as a part of the temporal-domain NLSE in optics. In this context, it is induced by the underlying interaction of the high-frequency envelope wave with a damped low-frequency wave mode. Also spatial inhomogeneity of the second-order dispersion (SOD) is assumed. As a result it is shown that the wavenumber downshift of solitons, caused by the pseudo-SRS, can be compensated with the upshift provided by decreasing SOD coefficients. Analytical results and numerical results are in a good agreement.