Modulational instability and kink, anti-kink, breather soliton for nonlocal reverse space time dispersive nonlinear Schrödinger equation

In this paper, we examine the soliton solutions of a new form of the nonlocal reverse space time dispersive nonlinear Schrödinger equation which describes the propagation of solitons in optical fiber. We also aim to understand the role of higher-order dispersion in the dynamics of solitons in optical fibers. Hence, the proposed equation is solved with the help of \(\Bigl (\frac{G^{\prime }}{G^2}\Bigr )\)-expansion method, and some novel solutions are presented for local and nonlocal field. The role of higher-order dispersion on the dynamics of the soliton in optical fiber is discussed both in the absence and in the presence of nonlinear dispersion. We analyze the physical parameters responsible for the evolution of local and nonlocal soliton solutions in optical fiber. We also explore the stability of solutions of dynamical equation using linear stability analysis. The stability of the soliton solutions is presented using the modulational instability gain, and the role of physical parameters on the stability of solutions is also discussed.