© 2022 Shanghai Jiaotong UniversityWe have analyzed the two coupled nonlinear Schrödinger equations (CNLSE) in the current work. This model has applications in high birefringence fibers. To generate different types of analytical solutions, including exponential, periodic, and soliton-type, we operated generalized Kudryashov, modified Kudryashov and exponential rational function procedures. Thanks to this implementation, we contributed to ocean engineering, plasma waves, nonlinear birefringence phenomena, and pulse compression features. In addition, in our article, we have included 2D and 3D graphics of solutions to help understand the physical meaning of solutions. The article highlights the method's ability to provide various solutions to various physical problems.