High-order coupled nonlinear Schrödinger equation and analyzing soliton dynamics in multimode fibers

The behavior of solitons in multimode fibers is investigated using the Connected Higher-Order Nonlinear Schrödinger Equations (CHNSE). A sophisticated algebraic technique is employed to analyze the CHNSE, yielding a variety of exact solutions, including bright and dark solitons, Weierstrass elliptic function solutions, periodic singular solutions, and hyperbolic and Jacobi elliptic solutions. These solutions are graphically represented using density and three-dimensional graphics to illustrate their physical characteristics. The CHNSE model provides deeper understanding of nonlinear optical processes in multimode fibers, essential for high-speed communication systems. The findings contribute to the development of new optical communication technologies.