21 citations · 22 across the 4 of their papers we have counts for
4 papers
Application of Lie Group-based Neural Network Method to Nonlinear Dynamical Systems
Ying Wen, Temuer Chaolu
In this paper, a Lie group-based neural network method is proposed for solving initial value problems of non linear dynamics. Due to its single-layer structure (MLP), the approach…
Solving the Initial Value Problem of Ordinary Differential Equations by Lie Group based Neural Network Method
Ying Wen, Temuer Chaolu, Xiangsheng Wang
To combine a feedforward neural network (FNN) and Lie group (symmetry) theory of differential equations (DEs), an alternative artificial NN approach is proposed to solve the initia…
The finite dimensional subalgebra classification of infinite dimensional symmetry algebra of two dimensional coupled nonlinear Schrödinger equations
YueXing Bai, Temuer Chaolu, Yan Li
The symmetry group structures of two dimensional coupled nonlinear Shrödinger equations are considered. We first show that the equations admit infinite dimensional symmetry algebra…
Approximate homotopy series solutions of perturbed PDEs via approximate symmetry method
Zhi-Yong Zhang
We show that the two couple equations derived by approximate symmetry method and approximate homotopy symmetry method are connected by a transformation for the perturbed PDEs. Cons…