Deriving Novel wave solutions to the (2+1)-dimensional fractional Paraxial wave dynamical equation with Kerr law using the $({G}'/G^2) $-expansion function technique

E. Abd Elbary, Fatma; Semary, Mourad S.; Fareed, ِِAisha F.; Elsesy, Mohammed A.

doi:10.22034/cmde.2025.64296.2908

Deriving Novel wave solutions to the (2+1)-dimensional fractional Paraxial wave dynamical equation with Kerr law using the $({G}'/G^2) $-expansion function technique

Document Type : Research Paper

Authors

¹ Faculty of Engineering, MTI university, Cario, Egypt.

² Basic Sciences Department, Faculty of Engineering, Badr University in Cairo, Cairo 11829, Egypt.

³ Department of Electrical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Al Kharj 16278, Saudi Arabia.

⁴ Department of Basic Engineering Sciences, Faculty of Engineering Benha, Benha university, Egypt.

10.22034/cmde.2025.64296.2908

Abstract

The method is used to find traveling wave solutions of nonlinear evolution equations (NLEEs), not "certain types". Specify "to find exact traveling wave solutions to certain types of nonlinear partial differential equations (NLPDEs)". In this case, the Paraxial Wave Dynamical Equation with Kerr law (PWDE) in the sense of the truncated $ \mathsf{M} $-fractional derivative. This equation is important in the study of wave propagation and optical phenomena. By employing this method, the researchers were able to obtain new, previously unknown exact solutions to this equation. These solutions represent different types of wave solutions, each with their own unique characteristics and properties. The significance of these novel wave solutions lies in their potential applications in physics and engineering. Wave phenomena play a crucial role in various fields, such as optics, photonics, and electromagnetics. The researchers indicate that these specific wave solutions have important practical applications in these domains. Moreover, we provide visual representations of the obtained solutions in the form of 3D, contour, and 2D plots. These graphical illustrations serve to demonstrate the feasibility and reliability of our proposed technique, showcasing its ability to capture the essential characteristics and behaviors of the solutions.

Keywords

Main Subjects

Fractional derivatives and integrals

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