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Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator 期刊论文
CHAOS SOLITONS & FRACTALS, 2022, 卷号: 165, 页码: 14
作者:  Zhong, Ming;  Yan, Zhenya
收藏  |  浏览/下载：71/0  |  提交时间：2023/02/07
Integrable fractional nonlinear wave equations  Fourier neural operator  Deep learning  Data-driven soliton mapping  Activation function  Channel of fully-connected layer  
Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes 期刊论文
PHYSICS LETTERS A, 2022, 卷号: 450, 页码: 15
作者:  Zhou, Zijian;  Wang, Li;  Yan, Zhenya
收藏  |  浏览/下载：80/0  |  提交时间：2023/02/07
Deep neural networks  B?cklund transform  Miura transform  Soliton equations  Breathers  Solitons  
The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions 期刊论文
APPLIED NUMERICAL MATHEMATICS, 2021, 卷号: 170, 页码: 298-320
作者:  Hou, Baohui;  Liang, Dong
收藏  |  浏览/下载：122/0  |  提交时间：2022/04/02
AVF method  CFD operator  Time high-order  Energy conservation  Convergence  Nonlinear wave equations  
Some special types of solutions of a class of the (N+1)-dimensional nonlinear wave equations 期刊论文
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 卷号: 56, 期号: 6, 页码: 1569-1579
作者:  Wang, Deng-Shan;  Yan, Zhenya;  Li, Hongbo
收藏  |  浏览/下载：120/0  |  提交时间：2018/07/30
sine-cosine-Gordon equation  double sinh-Gordon equation  separation transformation  Soliton solution  separation transformation approach  
Discrete exact solutions of modified Volterra and Volterra lattice equations via the new discrete sine-Gordon expansion algorithm 期刊论文
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 卷号: 64, 期号: 8, 页码: 1798-1811
作者:  Yan, ZY
收藏  |  浏览/下载：83/0  |  提交时间：2018/07/30
discrete soliton equations  discrete sine-Gordon expansion method  solitary wave solution  symbolic computation  
Numerical solution for series sine-Gordon equations using variational method and finite element approximation 期刊论文
APPLIED MATHEMATICS AND COMPUTATION, 2005, 卷号: 168, 期号: 1, 页码: 567-599
作者:  Wang, QF
收藏  |  浏览/下载：89/0  |  提交时间：2018/07/30
sine-Gordon equations  numerical solution  finite element methods  Gauss-Legendre quadrature  Runge-Kutta method  
New doubly periodic solutions of (2+1)-dimensional nonlinear wave equations via the generalized sine-Gordon equation expansion method 期刊论文
CHINESE JOURNAL OF PHYSICS, 2005, 卷号: 43, 期号: 1, 页码: 26-42
作者:  Yan, ZY
收藏  |  浏览/下载：106/0  |  提交时间：2018/07/30
A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations 期刊论文
CHAOS SOLITONS & FRACTALS, 2005, 卷号: 23, 期号: 3, 页码: 767-775
作者:  Yan, ZY
收藏  |  浏览/下载：87/0  |  提交时间：2018/07/30
The new constructive algorithm and symbolic computation applied to exact solutions of nonlinear wave equations 期刊论文
PHYSICS LETTERS A, 2004, 卷号: 331, 期号: 3-4, 页码: 193-200
作者:  Yan, ZY
收藏  |  浏览/下载：82/0  |  提交时间：2018/07/30
Sine-Gordon equation  nonlinear wave equation  symbolic computation  doubly periodic solution  solitary wave solution  
Exact travelling wave solutions for a class of nonlinear partial differential equations 期刊论文
CHAOS SOLITONS & FRACTALS, 2004, 卷号: 19, 期号: 5, 页码: 1113-1117
作者:  Xie, FD;  Gao, XS
收藏  |  浏览/下载：85/0  |  提交时间：2018/07/30