Smooth equivalence of differential equations and linear automorphisms

1999 ◽  
Vol 66 (4) ◽  
pp. 464-473
Author(s):  
V. S. Samovol
Keyword(s):  
Differential Equations ◽  
Equivalence Of Differential Equations

scholarly journals ON THE EQUIVALENCE OF DIFFERENTIAL EQUATIONS

2014 ◽  
Vol 4 (1) ◽  
pp. 103-114
Author(s):  
Zhengxin Zhou ◽  
◽  
Richang Tai ◽  
Fei Wang ◽  
Shuying Zong
Keyword(s):  
Differential Equations ◽  
Equivalence Of Differential Equations

scholarly journals On the Equivalence of Differential Equations in the Sense of Coincidence Reflecting Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Zhengxin Zhou
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
New Method ◽  
Reflecting Function ◽  
Polynomial Differential Equation ◽  
Equivalence Of Differential Equations

We use a new method for constructing some differential equations which are equivalent to a given equation in the sense of having the same reflecting function. We completely solve the problem: when is a polynomial differential equation equivalent to a given polynomial differential equation? Many sufficient conditions have been established for one differential equation to be equivalent to a given differential equation. We apply the obtained results to study the boundary value problem of two equivalent differential equations.

scholarly journals Equivalence of differential equations of order one

2015 ◽  
Vol 71 ◽  
pp. 47-59 ◽  
Author(s):  
L.X. Chau Ngo ◽  
K.A. Nguyen ◽  
M. van der Put ◽  
J. Top
Keyword(s):  
Differential Equations ◽  
Equivalence Of Differential Equations

scholarly journals Equivalence Conditions and Invariants for the General Form of Burgers’ Equations

2021 ◽  
Author(s):  
Mostafa Hesamiarshad
Keyword(s):  
Differential Equations ◽  
Burgers Equation ◽  
Equivalence Problem ◽  
Independent Variables ◽  
Burgers Equations ◽  
Structure Equations ◽  
Equivalence Of Differential Equations ◽  
Local Equivalence ◽  
Two Independent Variables ◽  
Contact Transformations

AbstractEquivalence of differential equations is one of the most important concepts in the theory of differential equations. In this paper, the moving coframe method is applied to solve the local equivalence problem for the general form of Burgers’ equation, which has two independent variables under action of a pseudo-group of contact transformations. Using this method, we found the structure equations and invariants of these equations, as a result some conditions for equivalence of them will be given.

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