scholarly journals The extension of Darboux's method to systems in involution of partial differential equations of arbitrary order in two independent variables

1973 ◽  
Vol 49 (10) ◽  
pp. 777-781
Author(s):  
Kunio Kakié
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Arbitrary Order ◽  
Partial Differential ◽  
Independent Variables ◽  
Darboux's Method ◽  
Two Independent Variables

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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