Applications of complete discrimination system approach to analyze the dynamic characteristics of the cubic–quintic nonlinear Schrodinger equation with optical soliton and bifurcation analysis

In this research, the complete discriminant system (CDS) of polynomial method (CDSPM) will be applied to analyze the dynamic characteristics of the cubic-quintic nonlinear Schrodinger equation (CQNLSE) with an additional anti-cubic nonlinear term (CQNLSE-AC) with a particular emphasis on the introduction of various optical solitons and wave structures. Our analysis of the CQNLSE-AC illustrates the importance of CDSPM, and we give dynamic results, such as critical conditions and bifurcation points for solutions. Additionally, we determine several types of optical soliton solutions, including Jacobian elliptic function (JEF), hyperbolic function, and trigonometric function solutions, and also convert JEF into solitary wave (SW) solutions.