scholarly journals A generalized integrability problem for G-structures

2015 ◽  
Vol 195 (5) ◽  
pp. 1463-1489 ◽  
Author(s):  
Andrea Santi
Keyword(s):  
Integrability Problem

scholarly journals On the integrability problem for systems of partial differential equations in one unknown function, I

2019 ◽  
Vol 11 (4) ◽  
pp. 35-71 ◽  
Author(s):  
Antonio Kumpera
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Unknown Function ◽  
Contact Structures ◽  
Partial Differential ◽  
Practical Applications ◽  
First Order ◽  
Integrability Problem ◽  
Integration Problem ◽  
In The Beginning

We discuss the integration problem for systems of partial differential equations in one unknown function and special attention is given to the first order systems. The Grassmannian contact structures are the basic setting for our discussion and the major part of our considerations inquires on the nature of the Cauchy characteristics in view of obtaining the necessary criteria that assure the existence of solutions. In all the practical applications of partial differential equations, what is mostly needed and what in fact is hardest to obtains are the solutions of the system or, occasionally, some specific solutions. This work is based on four most enlightening Mémoires written by Élie Cartan in the beginning of the last century.

The integrability problem for a class of planar systems

Nonlinearity ◽  
2009 ◽  
Vol 22 (2) ◽  
pp. 395-420 ◽  
Author(s):  
A Algaba ◽  
E Gamero ◽  
C García
Keyword(s):  
Integrability Problem ◽  
Planar Systems

scholarly journals On the Formal Integrability Problem for Planar Differential Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Antonio Algaba ◽  
Cristóbal García ◽  
Jaume Giné
Keyword(s):  
Algebraic Curves ◽  
Necessary Conditions ◽  
Differential Systems ◽  
Analytic Integrability ◽  
Integrability Problem ◽  
Formal Integrability

We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems inℂ2, and imposing the formal integrability we find resonant centers obviating the computation of some necessary conditions.

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