Optical soliton solutions in a distinctive class of nonlinear Schrödinger’s equation with cubic, quintic, septic, and nonic nonlinearities

The Biswas–Mollivic equation is a special type of nonlinear Schrödinger equation, which explains the spatio-temporal behaviour of excitable media. In this paper, we investigate the optical soliton solutions of the Biswas–Mollivic equation with cubic–quintic–septic–nonic nonlinearities using the generalized Riccati equation mapping method. This method is efficient and provides new perspectives. It also provides novel insights into the dynamics of excitable media. Our findings add to a better understanding of the complex spatio-temporal patterns that develop in excitable media and have potential applications in the design of new technologies for controlling and manipulating pattern formation. To depict optical soliton solutions graphically, we use the MATLAB software.