Propagation Of Optical Solitons In Optical Metamaterials And Generalized Non-local Dual Mediums

In nonlinear optics,mathematical models can effectively simulate the propagation of optical soliton dynamics.Among the numerous models that have emerged,the nonlinear Schr(?)dinger equation is one of the most common basic models,it not only has extensive applications in some important physical fields,but also can be well used to describe the propagation of optical solitons in nonlinear mediums.This paper focuses on the propagation of optical solitons of the nonlinear Schr(?)dinger equation in two different mediums.The first model is anti-cubic nonlinear Schr(?)dinger equation in optical metamaterials medium,by using trial equation method combined with the second-order complete discriminant system for polynomial,we obtain abundant propagation patterns,including rational patterns,trigonometric patterns,solitary wave patterns and Jacobi elliptic function double-periodic patterns.The second model is the nonlinear Schr(?)dinger equation with Kudryashov’s law of generalized non-local dual medium,the same trial equation method was applied,and then apply the simplified model to the fourth-order complete discriminant system for polynomial,we obtain three types of propagation patterns,which are the singular patterns,solitary wave patterns and Jacobi elliptic function double-periodic patterns.Among the optical wave patterns obtained from these two models,the Jacobi elliptic function double-period patterns are new results.Finally,we show the dynamic behaviors and temporal-space structures of these propagation patterns through the given two-dimensional and threedimensional modulus diagrams.