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

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	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
Computational Methods for Differential Equations
مقاله 27، دوره 14، شماره 3، مهر 2026، صفحه 1442-1457 اصل مقاله (6.78 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.64296.2908
نویسندگان
Fatma E. Abd Elbary¹؛ Mourad S. Semary²؛ ِِAisha F. Fareed^* ³؛ Mohammed A. Elsesy⁴
¹Faculty of Engineering, MTI university, Cario, Egypt.
²Basic Sciences Department, Faculty of Engineering, Badr University in Cairo, Cairo 11829, Egypt.
³Department of Electrical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Al Kharj 16278, Saudi Arabia.
⁴Department of Basic Engineering Sciences, Faculty of Engineering Benha, Benha university, Egypt.
چکیده
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.
کلیدواژه‌ها
Fractional calculus؛ the truncated M-fractional derivative؛ Exact solutions؛ (G′/G2)-expansion function method؛ Paraxial Wave Dynamical Equation (PWDE)

مراجع
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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