Nonlinear Dynamics - A new method named bilinear neural network is introduced in this paper, and the corresponding tensor formula is proposed to obtain the exact analytical solutions of nonlinear... 相似文献
Although many effective methods for solving partial differential equations (PDEs) have been proposed, there is no universal method that can solve all PDEs. Therefore, solving partial differential equations has always been a difficult problem in mathematics, such as deep neural network (DNN). In recent years, a method of embedding some basic physical laws into traditional neural networks has been proposed to reveal the dynamic behavior of equations directly from space-time data [i.e., physics-informed neural network (PINN)]. Based on the above, an improved deep learning method to recover the new soliton solution of Huxley equation has been proposed in this paper. As far as we know, this is the first time that we have used an improved method to study the numerical solution of the Huxley equation. In order to illustrate the advantages of the improved method, we use the same network depth, the same hidden layer and neurons contained in the hidden layer, and the same training sample points. We analyze the dynamic behavior and error of Huxley’s exact solution and the new soliton solution and give vivid graphs and detailed analysis. Numerical results show that the improved algorithm can use fewer sample points to reconstruct the exact solution of the Huxley equation with faster convergence speed and better simulation effect.
In this paper, an extended simplest equation method is proposed to seek exact travelling wave solutions of nonlinear evolution equations. As applications, many new exact travelling wave solutions for several forms of the fifth-order KdV equation are obtained by using our method. The forms include the Lax, Sawada-Kotera, Sawada-Kotera-Parker-Dye, Caudrey-Dodd-Gibbon, Kaup-Kupershmidt, Kaup-Kupershmidt-Parker-Dye, and the Ito forms. 相似文献
In the present study, laser ablation inductively coupled plasma atomic emission spectroscopy (LA-ICP-AES) was successfully used to classify 26 ancient potash glass beads. These samples, mainly dated from the Han Dynasty to the Jin Dynasty, were from several provinces of both China and Vietnam. Quantitative analyses were done with both weathered and polished samples in order to consider the effects of surface weathering. Based on the characteristics of major, minor, and trace elements, we divided the samples into three subgroups (the percentage for each subgroup was 50%, 42%, and 8%, respectively) and also determined their main colorants. The results obtained provide new clues to trace the possible producing centers of ancient potash glasses in Asia. This study also reveals a complex network related to the trade of ancient potash glasses. 相似文献
Nonlinear Dynamics - With the development of computers and neural networks, the traditional methods of solving differential equations have been greatly developed. Typical examples are the... 相似文献
Nonlinear Dynamics - In this paper, we obtained a kind of lump solutions of ( $$2+1$$ )-dimensional bSK equation with the assistance of Mathematica by using the Hirota bilinear method. These lump... 相似文献