Nonlinear dispersion in parabolic law medium and its optical solitons

This paper studies the optical soliton solutions of a nonlinear Schrödinger equation (NLSE) involving parabolic law of nonlinearity with the presence of nonlinear dispersion by using the generalized auxiliary equation technique. As a result, new varieties of exact traveling wave solutions have been uncovered, comprising of the hyperbolic trigonometric, trigonometric, exponential, and rational. Interestingly, we obtain the bright, dark, periodic, singular, and other soliton solutions to the nonlinear model. Some of the achieved solutions are illustrated graphically in order to fully understand their physical behaviour. Furthermore, the findings discussed in this present investigation may be useful in explaining the propagation of optical solitons in a weakly nonlocal parabolic law medium.