Efficient Analytic Technique for Fractional Fourth-Order Cubic Nonlinear Schrodinger Equation

This paper presents an advanced analytical solution for the fractional fourth-order dispersive cubic nonlinear Schrödinger equation (DNLS), a model significant for engineering applications in optical fiber systems, quantum mechanics, and plasma physics. This work leverages the qhomotopy analysis transform method (q-HATM) to address the challenges in modeling complex, nonlinear wave propagation in engineering and physics applications involving fractional dynamics. By providing highly accurate, convergent solutions, this method allows engineers and scientists to model memory effects and higher-order dispersions more effectively in systems like optical waveguides and plasma waves. The demonstrated accuracy and convergence of q-HATM establish it as a practical tool for researchers aiming to solve complex wave propagation problems, advancing both theoretical understanding and real-world engineering solutions in nonlinear optics, quantum fields, and other areas requiring precise modeling of wave interactions.OPEN ACCESS Received: 25/10/2024 Accepted: 05/03/2025 Published: 20/04/2025