New soliton solutions with graphical analysis to the fractional Schrödinger–Hirota equation

Document Type : Research Articles

Author

Department of Mathematics, Faculty of Sciences, Gonbad Kavous University, Gonbad, Iran

10.22080/cjms.2026.30583.1779

Abstract

The central objective of this study is to employ the
generalized exponential rational function method in order to derive
exact analytical solutions for the generalized nonlinear fractional
Schr¨odinger–Hirota equation. By applying various ansatz
techniques with time-dependent coefficients, both bright and dark
optical soliton solutions of the proposed model are systematically
constructed and analyzed. These soliton structures highlight the
rich dynamical behavior of the equation and demonstrate the effectiveness
of the adopted analytical approach. Furthermore, a detailed
graphical investigation of the obtained solutions is carried out
using Mathematica software. This visual analysis provides deeper
insight into the evolution, stability, and fluctuation characteristics
of the solutions under different parameter settings, thereby enhancing
the physical interpretation of the results. The outcomes of this
research have potential applications in the development of advanced
theoretical models in plasma physics, condensed matter physics, optical
fiber communications, and various industrial processes.

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