Numerous Exact Two-Pick, M-Shaped, and W-Shaped Solutions of Wavelength-Division-Multiplexed Channels of Optical Fibre Transmission Systems Described by Coupled Nonlinear Schrödinger Equations

The coupled nonlinear Schrödinger equation, which appears as a model explaining the interactions between pulses in wavelength-division-multiplexed channels of optical fibre transmission systems, is studied in three different scenarios of solitons interactions. The travelling transformation is used to convert them into a stationary form, or nonlinear ODE. Then, RCAM is used to solve three different integrable cases of these systems. For every one of these generated solution’s boundedness requirements, three theorems are proposed and independently proven. To confirm the validity of the theorems, a few specific values of the parameters that meet the requirements of the theorems are taken, plotted, and different soliton profiles of the system are analysed. This study presents, for the first time, the appearance criteria for the W-shape, M-shape, and double-pick structure solition profiles together with their optimal locations. We investigate the ways in which the existence of several optima points governs the shape of solutions that emerge as multiple two-pick, M-shaped, and W-shaped solitons. The findings of the research may be useful in the development of birefringence controlled switching and bright and dark soliton fibre lasers.