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Your search keyword '"Run-Fa Zhang"' showing total 6 results
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6 results on '"Run-Fa Zhang"'

1. Numerical simulation and theoretical analysis of pattern dynamics for the fractional-in-space Schnakenberg model.

Author

Ji-Lei Wang, Yu-Xing Han, Qing-Tong Chen, Zhi-Yuan Li, Ming-Jing Du, Yu-Lan Wang, Run-Fa Zhang, and Dan Tian

Subjects
PATTERNS (Mathematics), SEPARATION of variables, NONLINEAR analysis, LAPLACIAN operator, NUMERICAL analysis
Abstract

Effective exploration of the pattern dynamic behaviors of reaction-diffusion models is a popular but difficult topic. The Schnakenberg model is a famous reaction-diffusion system that has been widely used in many fields, such as physics, chemistry, and biology. Herein, we explore the stability, Turing instability, and weakly non-linear analysis of the Schnakenberg model; further, the pattern dynamics of the fractional-in-space Schnakenberg model was simulated numerically based on the Fourier spectral method. The patterns under different parameters, initial conditions, and perturbations are shown, including the target, bar, and dot patterns. It was found that the pattern not only splits and spreads from the bar to spot pattern but also forms a bar pattern from the broken connections of the dot pattern. The effects of the fractional Laplacian operator on the pattern are also shown. In most cases, the diffusion rate of the fractional model was higher than that of the integer model. By comparing with different methods in literature, it was found that the simulated patterns were consistent with the results obtained with other numerical methods in literature, indicating that the Fourier spectral method can be used to effectively explore the dynamic behaviors of the fractional Schnakenberg model. Some novel pattern dynamics behaviors of the fractional-in-space Schnakenberg model are also demonstrated. [ABSTRACT FROM AUTHOR]

Published
2024
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5. Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo–Miwa equation

Author

Hui-Min Yin, Mingchu Li, and Run-Fa Zhang

Subjects
Physics, Partial differential equation, Artificial neural network, Applied Mathematics, Mechanical Engineering, One-dimensional space, Mathematical analysis, Aerospace Engineering, Bilinear interpolation, Ocean Engineering, 01 natural sciences, Nonlinear system, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Control and Systems Engineering, Contour line, 0103 physical sciences, Test functions for optimization, Electrical and Electronic Engineering, Rogue wave, 010301 acoustics
Abstract

It is well known that most classical test functions to solve nonlinear partial differential equations can be constructed via single hidden layer neural network model by using Bilinear Neural Network Method (BNNM). In this paper, the neural network model of test function for the (3+1)-dimensional Jimbo–Miwa equation is extended to the “4-2-3” model. By giving some specific activation functions, new test function is constructed to obtain analytical solutions of the (3+1)-dimensional Jimbo–Miwa equation. Rogue wave solutions and the bright and dark solitons are obtained by giving some specific parameters. Via curve plots, three-dimensional plots, contour plots and density plots, dynamical characteristics of these waves are exhibited.

Published
2021
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6. Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation

Author

Run-Fa Zhang, Fu-Chang Zheng, Mohammed Albishari, Zhong-Zhou Lan, and Mingchu Li

Subjects
0209 industrial biotechnology, Artificial neural network, Applied Mathematics, One-dimensional space, Bilinear interpolation, 020206 networking & telecommunications, 02 engineering and technology, Symbolic computation, Computational Mathematics, Nonlinear Sciences::Exactly Solvable and Integrable Systems, 020901 industrial engineering & automation, Electromagnetism, Contour line, 0202 electrical engineering, electronic engineering, information engineering, Fluid dynamics, Applied mathematics, Rogue wave, Mathematics
Abstract

Under investigation in this paper is the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like (CDGKS-like) equation. Based on bilinear neural network method, the generalized lump solution, classical lump solution and the novel analytical solution are constructed by giving some specific activation functions in the single hidden layer neural network model and the “3-2-2” neural network model. By means of symbolic computation, these analytical solutions and corresponding rogue waves are obtained with the help of Maple software. These results fill the blank of the CDGKS-like equation in the existing literature. Via various three-dimensional plots, curve plots, density plots and contour plots, dynamical characteristics of these waves are exhibited. The effective methods used in this paper is helpful to study the nonlinear evolution equations in plasmas, mathematical physics, electromagnetism and fluid dynamics.

Published
2021
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