Numerous Analytical Solutions to a (2 + 1)-Dimensional Schrödinger Equation with Variable Coefficients in Inhomogeneous Media

Nonlinear partial differential equations are one of the important branches of modern mathematics, with many important values in both theory and practical applications. In recent years, with the development of fiber optic communication technology, research on information transmission in optical fibers has become increasingly in-depth. Among them, due to the excellent stability of the solutions to the nonlinear Schrödinger equation, it has attracted considerable attention from researchers, and its different types of solutions have become the top priority of research. Via this investigation, novel precise solutions of a (2 + 1)-dimensional variable coefficients Schrödinger equation used in inhomogeneous media have been acquired. Utilizing the support of the unified method, the polynomial solutions have been obtained successfully. Through the other three methods, we can secure some new different complex traveling wave solutions. Additionally, the illustrations portraying some solutions have been presented. At last, we present a comprehensive overview of the attributes comprising these solutions.