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.

scholarly journals On the differential equations of H. Lewy

1961 ◽  
Vol 2 (1) ◽  
pp. 11-16
Author(s):  
W. B. Smith-White
Keyword(s):  
Differential Equations ◽  
Special Form ◽  
Linear Equations ◽  
Systems Of Equations ◽  
Independent Variables ◽  
Image Position ◽  
Two Independent Variables

It is known that the theory of Cauchy's problem for differential equations with two independent variables is réducible to the corresponding problem for systems of quasi-linear equations. The reduction is carried further, by means of the theory of characteristics, to the case of systems of equations of the special form first considered by H. Lewy [1]. The simplest case is that of the pair of equationswhere the aii depend on z1 and z2. The problem to be considered is that of finding functions z1(x, y), z2(x, y) which satisfy (1) and which take prescribed values on x + y = 0.

scholarly journals An integrable system of partial differential equations on the special linear group

2002 ◽  
Vol 44 (1) ◽  
pp. 83-93
Author(s):  
Peter J. Vassiliou
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Group ◽  
Special Linear Group ◽  
Partial Differential ◽  
Special Linear ◽  
First Order ◽  
Independent Variables ◽  
Two Independent Variables

AbstractWe give an intrinsic construction of a coupled nonlinear system consisting of two first-order partial differential equations in two dependent and two independent variables which is determined by a hyperbolic structure on the complex special linear group regarded as a real Lie groupG. Despite the fact that the system is not Darboux semi-integrable at first order, the construction of a family of solutions depending.upon two arbitrary functions, each of one variable, is reduced to a system of ordinary differential equations on the 1-jets. The ordinary differential equations in question are of Lie type and associated withG.

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