Modulation instability analysis and optical solitary waves solutions of high-order dispersive parabolic Schrödinger–Hirota equation

The balance of nonlinearity and dispersion in optical fiber medium gives rise to a constantly propagating pulse. Such distortion less waves have attracted potential interest. The dynamics of optical solitons are governed by the nonlinear Schrödinger’s equation (NLSE). A modified form of NLSE which incorporates group velocity dispersion (GVD) and the Kerr law nonlinearity is recently adopted for the study of such waves. Here, we investigate the nonlinear Schrödinger–Hirota’s equation (NLSHE) using the Sardar subequation approach. Some novel solutions to the NLSHE corresponding to the bright, dark, kink, and cusp solitons have been reported. Additionally, the spatial and temporal dynamics of these solitons provide deep insight into the behavior of these solutions. The stability study is carried out via modulation instability (MI) concept. Our work might have benefits in the propagation of these pulses in the optical fiber for communication.