On the examination of optical soliton pulses of Manakov system with auxiliary equation technique

Purpose: This manuscript addresses to investigate the optical soliton solution of the Manakov model which governs soliton transmission technology by utilizing the auxiliary equation technique. Methodology: After obtaining the nonlinear ordinary differential equation form (NODE) of investigated nonlinear partial differential equation problem (NLPDE) with the complex wave transform (cWT), the serial form is suggested in accordance with the utilized auxiliary method, and after written in the NODE form, the linear algebraic system is formed and by aid of the any symbolic calculation package the unknown parameters are obtained. In order to gain the soliton solutions, the proposed series form, the solution functions of the method, and the cWT are brought together and it is checked that the obtained solutions satisfy the main equation. By considering the functions that satisfy the main equation as solutions, graphical presentations are made and interpreted in order to better understand the obtained results.Findings: By applying the effective auxiliary equation method, optical soliton pulse solutions such as bright, singular, V-shaped, periodic singular, periodic bright, periodic bright-dark have been obtained, and it has been shown that the method can be applied effectively for such equations.Originality: The auxiliary equation method has not been applied to the Manakov model and the V-shaped, periodic singular, periodic bright soliton pulse solutions have not been reported before.

Automated summary

This manuscript investigates the optical soliton solution of the Manakov model using the auxiliary equation technique. By obtaining the nonlinear ordinary differential equation form and solving the linear algebraic system, the unknown parameters are obtained. The findings show that the effective auxiliary equation method can successfully obtain various types of soliton pulse solutions.