Abstract

This article uses the enhanced direct algebraic method (EDAM) to study the exact traveling wave solutions of the paraxial wave equation with conformable fractional derivative. This method is selected due to its algorithmic simplicity, computational efficiency, and unique capability to yield diverse solution types within a unified algebraic framework. Firstly, the paraxial wave equation with conformable fractional derivative is transformed into an ordinary differential equation through traveling wave transformation. Then, the EDAM is systematically applied to construct accurate traveling wave solutions including twisted solitons, bell-shaped solitons, singular solitons, Weierstrass elliptic function solutions, and Jacobi elliptic function solutions, demonstrating the method’s superiority in handling complex nonlinear structures compared to standard expansion techniques. Finally, based on Matlab software to draw three-dimensional and two-dimensional graphs of partial solutions, these graphs intuitively demonstrate the regulatory effect of the fractional-order parameter α on waveform localization and amplitude. Specifically, as α increases, the soliton localization weakens and the wave packet broadens, providing insights into the dispersion management in optical fibers. The method used in this article is characterized by simple operation and rich solution types, providing an effective approach for studying fractional nonlinear partial-differential equations.

IPC Classification

Keywords