Novel Exact Analytical Solutions of the (3+1)-dimensional Potential Yu-toda-sasa-fukuyama Equation Via Lie Symmetry Analysis and Neural Network Models
Year: 2026
Type: article
Abstract: A novel method combining Lie symmetry analysis and neural network model is proposed for solving the (3+1)-dimensional potential-Yu-Toda-Sasa-Fukuyama (pYTSF) equation in this paper. This method has three processes: Firstly, the dimension of the given equation are reduced and two reduction equations are derived via Lie symmetry analysis; secondly, different test functions are constructed based on neural network models and various activation functions to yield solutions of the reduction equations; finally, a series of exact solutions of the original equation is achieved depending on the expression of group-invariant solutions and the transformation of variables. 12 novel exact analytical solutions of the (3+1)-dimensional pYTSF equation are obtained by the novel method. Furthermore, the dynamical characteristics of all solutions are illustrated by choosing appropriate parameters. The results validate the feasibility of this new method and show that the novel method may be applied in more nonlinear partial differential equations.
DOI: 10.11948/20250287
Authors: Yunjie Yang, Jianping Shi, Hui Fang
Institution: Kunming University of Science and Technology
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Award: （n+1)维非线性耦合波方程的解析解和稳定性问题研究
OpenAlex ID: W7203833419