The Sardar sub-equation technique for obtaining some optical solitons of cubic nonlinear Schrödinger equation involving beta derivatives with Kerr law nonlinearity

This study investigates new optical and chirped optical solitons for the space-time fractional cubic nonlinear Schrödinger equation using the Sardar sub-equation technique in the presence of Kerr law nonlinearity. The solutions are expressed in terms of hyperbolic and trigonometric functions, revealing a diverse range of behaviors within the system. The identified optical and chirped optical soliton types include dark, bright, kink, and periodic, showcasing a rich spectrum of phenomena. Representing soliton solutions using 2D and 3D graphs with varying parameters leads to a better understanding of their formation and characteristics. The findings contribute to the comprehension of nonlinear dynamics, offering insights into phenomena relevant to nonlinear optics, quantum mechanics, and condensed matter physics.