Unveiling optical solitons: Solving two forms of nonlinear Schrödinger equations with unified solver method

Abstract

The motivation of this work is to attain optical solitons of the generalized third-order nonlinear Schrödinger equation (NLSE) and the integrable (2+1)-dimensional coupled nonlinear Schrödinger equation (CNLSE). These models have various applications, including ultra-short pulses in optical fibers, making them noteworthy in applied sciences and mathematical physics. To extract the optical solitons of these models, the unified solver method (USM) is applied. The USM is a mathematically modified version of the Riccati equation and its related solutions. A unique advantage of this method is the elimination of the need for a balancing constant, simplifying the analytical process and enhancing the utility of these soliton solutions in practical applications. The obtained solutions include dark, singular, and periodic singular soliton solutions, enriching the understanding of optical solitons. In addition to the analytical solutions, the article also includes graphical representations to visually depict the obtained soliton solutions. These visualizations enhance the understanding and provide a clear picture of how the solitons behave in the given system.