Numerous Chirped and Optical Solitons for Cubic Nonlinear Schrödinger Equation with Kerr Nonlinearity and Beta Derivatives

Abstract This work explores new optical and chirped optical solitons for the space-time fractional cubic nonlinear Schrödinger equation (NLFSEs) in the presence of Kerr law nonlinearity, utilizing the new extended auxiliary equation approach. The solutions show a wide range of behaviors within the system and are stated in terms of trigonometric and hyperbolic functions. A broad range of phenomena is displayed by the several varieties of optical and chirped optical solitons that have been found, including dark, bright, kink, and periodic. A better knowledge of solution creation and properties may be attained by representing 2D and 3D graphs with different values of parameters.