Abstract
High-dimensional fractional equations research is a cutting-edge field with significant practical and theoretical implications in mathematics, physics, biological fluid mechanics, and other fields. Firstly, in this paper, the (4 + 1)-dimensional time-fractional Fokas equation in a higher-dimensional integrable system is studied by using semi-inverse and fractional variational theory. Then, the Lie symmetry analysis and conservation law analysis are carried out for the higher dimensional fractional order model with the symmetry of fractional order. Finally, the fractional-order equation is solved using the bilinear approach to produce the rogue wave and multi-soliton solutions, and the fractional equation is numerically solved using the Radial Basis Functions (RBFs) method.
Highlights
Fractional calculus [1,2] is a new research field in science and engineering, and it is widely used in physical mathematics, medicine, signal processing, liquid and gas fluctuation, and other fields
Based on the solution Equation (48) of the (4 + 1)-dimensional fractional Fokas equation obtained by the bilinear method, the phenomenon of rogue waves in higher dimensional higher-order Fokas model is studied
We use the numerical solution obtained by the Radial Basis Functions (RBFs) method and the exact solution obtained by the bilinear method
Summary
Fractional calculus [1,2] is a new research field in science and engineering, and it is widely used in physical mathematics, medicine, signal processing, liquid and gas fluctuation, and other fields. The numerical solution of the time-fractional Fokas equation is obtained using the Radial Basis Function (RBF) method [34] in this work. In. Section 4, we use the simplified bilinear method to obtain the rogue wave solution and soliton solution of (4 + 1)-dimensional time-fractional order Fokas. We obtain the Lagrange form of the Fokas equation of integer order as follows: L(v, v x , vt , vy , v xx , v xy , vzw , v xxxy , v xyyy ). Compared with the integer order model, the Equation (13) is more general and has potential value for the study of some properties in practical problems
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
