Abstract
The aim of this research intends to investigate the complex wave patterns and dynamic behavior of the Gerjikov-Ivanov equation (GIE), commonly known as the derivative nonlinear Schrödinger equation (DNLSE). The GIE model is the one that examines dynamics of optical soliton propagation for transmission technologies, including transcontinental and transoceanic lengths of optical fibers, data transfer, and the telecommunications sector. The GIE equation can be regarded as an extension of the NLSE when certain higher-order nonlinear effects are taken into account. We study various optical soliton solutions, including Jacobian elliptic, hyperbolic, and trigonometric functions, are identified using the polynomial method’s complete discrimination system (CDSPM). In addition, Jacobian elliptic functions can be transformed into solitary wave solutions. We also discuss bifurcation points, sensitivity analysis and critical solution conditions, offering a thorough grasp of the system’s dynamic features. The CDSPM plays an important role in studying equilibrium points, phase diagrams, bifurcation behavior, and performing quantitative and qualitative evaluations.
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