We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
A high dimensional evolution model and its rogue wave solution, breather solution and mixed solutions.
- Authors
Bai, Shuting; Yin, Xiaojun; Cao, Na; Xu, Liyang
- Abstract
In this study, a bilinear neural network method is used to solve the exact solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili equation, which is a new geophysical fluid mechanics model. This equation is derived from Charney equation of geomagnetic field by integrating the multiscale expansion and the perturbation method. To obtain the exact solutions of the model, we built test functions by using the bilinear neural network method. Compared to conventional methods, this method is shown to have faster results and better accuracy. Based on the construction of single-layer models, the rational solution, rogue wave solution, breather type solution and mixed solutions are obtained, and exact solution is also produced based on double-layer models. By increasing the number of activation functions or the number of layers in a neural network, the method's effectiveness is tested from different angles, and more importantly, the method of solving nonlinear equations is expanded. Then, various three-dimensional graphs, contour plots, and density plots with time and selection of activation function are used to depict the typical evolution of these waves.
- Subjects
ROGUE waves; NONLINEAR equations; FLUID mechanics; KADOMTSEV-Petviashvili equation; GEOMAGNETISM; ANGLES
- Publication
Nonlinear Dynamics, 2023, Vol 111, Issue 13, p12479
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-023-08467-x