scholarly journals Bäcklund transformations and zero‐curvature representations of systems of partial differential equations

1994 ◽  
Vol 35 (5) ◽  
pp. 2463-2484 ◽  
Author(s):  
Friedemann Brandt
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Bäcklund Transformations ◽  
Partial Differential ◽  
Zero Curvature ◽  
Backlund Transformations

Quasi-Lie schemes for PDEs

2019 ◽  
Vol 16 (07) ◽  
pp. 1950096 ◽  
Author(s):  
J. F. Cariñena ◽  
J. Grabowski ◽  
J. de Lucas
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bäcklund Transformations ◽  
Partial Differential ◽  
First Order ◽  
Backlund Transformations ◽  
Integrability Conditions ◽  
Lie Systems ◽  
Abel Differential Equations

The theory of quasi-Lie systems, i.e. systems of first-order ordinary differential equations that can be related via a generalized flow to Lie systems, is extended to systems of partial differential equations (PDEs) and its applications to obtain [Formula: see text]-dependent superposition rules, and integrability conditions are analyzed. We develop a procedure of constructing quasi-Lie systems through a generalization to PDEs of the so-called theory of quasi-Lie schemes. Our techniques are illustrated with the analysis of Wess–Zumino–Novikov–Witten models, generalized Abel differential equations, Bäcklund transformations, as well as other differential equations of physical and mathematical relevance.

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