Dual-mode optical solitons and modulation instability analysis of Schrödinger-Hirota equation incorporating spatio-temporal dispersion

This paper proposes two novel extensions of the nonlinear Schrodinger’s equation in dual-mode with Kerr and parabolic nonlinearities. These two models with spatiotemporal dispersion are investigated by the robust tanh and Kudryashov method. Different kinds of dual-mode optical solitons, such as singular and dark solutions, are retrieved alongside the parametric constraint conditions. The physical attributes of these solutions with both Kerr and parabolic nonlinearities are studied utilizing 3D and 2D graphs. Moreover, modulation instability analysis for Schrodinger’s equation with parabolic nonlinearity is carried out. The influence of incident power and nonlinear coefficients on the gain spectrum is studied and highlighted through graphs.