Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme

This research investigates the numerical computation of cubic-quartic optical solitons in birefringent fibers in accordance with Kerr's law. Utilizing the Improved Adomian Decomposition Method (IADM), the study improves the solution of complex-valued nonlinear evolution equations. It identifies a strong correlation between numerical results and earlier analytical soliton expressions from Zahran and Bekir. The analysis highlights impressively low computational errors, confirming IADM's effectiveness in delivering accurate solutions. This method decomposes both linear and nonlinear differential equations into simpler sub-problems, enabling the extraction of approximate analytical solutions without the need for linearization or perturbation techniques. IADM's adaptability suggests its potential for application in various domains, particularly in the optimization and design of optical communication systems.•The research utilizes both the Adomian Decomposition Method (ADM) and its enhanced version (IADM) to solve the Gerdjikov-Ivanov equation.•Numerical simulations validate the accuracy and stability of these methods, with IADM showing superior convergence.•The study underscores the importance of these methods in improving optical communication systems and other nonlinear applications.