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. In addition, spatial inhomogeneity of the secondorder 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.