Symmetry Reduction of Ordinary Differential Equations Using Moving Frames

2018 ◽  
Vol 25 (2) ◽  
pp. 211-246
Author(s):  
Francis Valiquette
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Symmetry Reduction ◽  
Moving Frames

Families of analytic solutions for (2+1) model in unbounded domain via optimal Lie vectors with integrating factors

2019 ◽  
Vol 33 (20) ◽  
pp. 1950229 ◽  
Author(s):  
R. Sadat ◽  
M. M. Kassem ◽  
Wen-Xiu Ma
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Unbounded Domain ◽  
Analytic Solutions ◽  
Symmetry Reduction ◽  
Lie Symmetry ◽  
Two Stages ◽  
Integrating Factors

Through the commutator table and the adjoint table between the infinitesimals, we apply two stages of Lie symmetry reduction to reduce the (2[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation to ordinary differential equations (ODE’s). Some of these ODE’s had no quadrature. We derive several new solutions for these non-solvable ODE’s using Integrating Factors property.

scholarly journals Numerical Simulation and Symmetry Reduction of a Two-Component Reaction-Diffusion System

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Jina Li ◽  
Xuehui Ji
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Reaction Diffusion ◽  
Symmetry Reduction ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Symmetry Classification ◽  
Two Component

In this paper, the symmetry classification and symmetry reduction of a two-component reaction-diffusion system are investigated, the reaction-diffusion system can be reduced to system of ordinary differential equations, and the solutions and numerical simulation will be showed by examples.

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