Breather-like soliton, M-shaped profile, W-shaped profile, and modulation instability conducted by self-frequency shift of the nonlinear Schrodinger equation

Abstract

We study the behavior of an optical soliton of the nonlinear Schrodinger equation (NLSE) with spatiotemporal, self-steepening (SS), self-frequency shift (SFS), and Kerr nonlinearity (Kn) terms. We use the traveling wave transformation to point out the constraint relation. To investigate the robustness of the analytical results, we employ the generalized Kudryashov method and a different form of Jacobi's elliptic function method (JEFM). We have exhibited the breather-like soliton, M-shaped profile, W-shaped profile, and several other Jacobi elliptic function solutions. We examine the effects of the nonlinear dispersion coefficients and the group velocity dispersion on the modulation instability (MI) bands in anomalous and normal dispersion regimes. The generation of the MI growth rate with the variation of the nonlinear dispersion is noted. These results could improve the communication in optical fibers.