A comprehensive analysis of Fokas–Lenells equation using Lie symmetry method

Abstract

This article extracts analytical solutions of the Fokas–Lenells equation describing pulse propagation in optical fibers and presents a comprehensive analysis of the analytical solutions. This paper focuses on deriving analytical, non‐perturbative solutions for the Fokas–Lenells equation by reducing it to a system of ordinary differential equations using the Lie symmetry method. Three generators for the Lie algebra are obtained, and three reductions are explored by combining vector generators. These algebraic structures provide a powerful framework for simplifying complex mathematical and physical problems by revealing underlying symmetries and patterns. The graphical representations of obtained solutions are rendered. Besides, the influence of parameters within the equation on the behavior of the solutions has been demonstrated in the figures. These results contribute to a deeper understanding of the Fokas–Lenells equation and have implications in various fields of physics and engineering.

Analyzing the American portfolio options within the CEV model incorporating dividend yield by the Lie symmetry approach

“…It is beyond the scope of this research to discuss the step-by-step solution scheme of the Lie symmetry method and its applications. For a better understanding, readers are recommended to study the references mentioned in [6,29,11,34,9,32,46,27,19] and the related literature within. Gazizov and Ibragimov [15] were among the early researchers who explored the Lie symmetry approach for the classical Black-Scholes problem and discovered group invariant solutions.…”