New dynamical behaviors and soliton solutions of the coupled nonlinear Schrödinger equation

In this work, we mainly investigate the coupled nonlinear Schrödinger type equation,which is employed to elaborate the propagation of waves in different fields like Bose–Einstein condensations (BEC) in plasma physics, ultra-short pulses in birefringent fibers and pressure pulses in artery vessels. The study of multi-component equations has gained significant interest due to their ability to elucidate complex physical phenomena and exhibit dynamic structures of localized wave solutions. Diverse novel soliton solutions of the coupled nonlinear Schrödinger type equation are successfully constructed via the unified solver method and improved F-expansion method. The dynamic behaviors of these obtained solutions are elaborated by sketching some three-dimensional (3D) and two-dimensional (2D) graphs. The two efficient mathematical approaches can be widely employed to solve other types of nonlinear partial differential equations (NLPDEs).