### Citations

312 |
Leçons sur la théorie générale des surfaces. 2ème partie, Paris: Gauthiers–Villars, 1889. 15 Dijkgraaf, R.: Intersection theory, integrable hierarchies and topological field theory. Lecture Notes at Cargese Summer School
- Darboux
- 1991
(Show Context)
Citation Context ... numerous examples of Darboux integrable systems. 1 1 Decomposable exterior differential systems 2 Introduction Darboux integrability of second order scalar equations was introduced by Gaston Darboux =-=[5, 6]-=-. Generalizations to many other systems are known, such as first order systems [13], hyperbolic exterior differential systems [3] and elliptic equations [10]. An important step in the classification o... |

22 | Hyperbolic exterior differential systems and their conservation laws
- Bryant, Griffiths, et al.
- 1995
(Show Context)
Citation Context ...y of second order scalar equations was introduced by Gaston Darboux [5, 6]. Generalizations to many other systems are known, such as first order systems [13], hyperbolic exterior differential systems =-=[3]-=- and elliptic equations [10]. An important step in the classification of Darboux integrable equations was given by Vessiot in the papers [14, 15]. Vessiot associates to each second order equation Darb... |

16 | Characteristics and the geometry of hyperbolic equations in the plane - Gardner, Kamran - 1993 |

11 | Vessiot structure for manifolds of (p, q)-hyperbolic type: Darboux integrability and symmetry
- Vassiliou
(Show Context)
Citation Context .... We give a geometric construction of the Lie algebras of tangential symmetries associated to the Darboux integrable systems. This construction has the advantage over previous constructions [14, 15], =-=[12, 13]-=- that our construction does not require the use of adapted coordinates and works for arbitrary dimension of the underlying manifold. In particular it works for the prolongations of decomposable exteri... |

9 |
Tangential characteristic symmetries and first order hyperbolic systems
- Vassiliou
- 2001
(Show Context)
Citation Context .... We give a geometric construction of the Lie algebras of tangential symmetries associated to the Darboux integrable systems. This construction has the advantage over previous constructions [14, 15], =-=[12, 13]-=- that our construction does not require the use of adapted coordinates and works for arbitrary dimension of the underlying manifold. In particular it works for the prolongations of decomposable exteri... |

7 |
Sur les équations aux dérivées partielles du second ordre
- Darboux
(Show Context)
Citation Context ... numerous examples of Darboux integrable systems. 1 1 Decomposable exterior differential systems 2 Introduction Darboux integrability of second order scalar equations was introduced by Gaston Darboux =-=[5, 6]-=-. Generalizations to many other systems are known, such as first order systems [13], hyperbolic exterior differential systems [3] and elliptic equations [10]. An important step in the classification o... |

7 |
les équations aux dérivées partielles du second ordre, F (x, y, z, p, q, r, s, t) = 0, intégrables par la méthode de Darboux
- Sur
- 1942
(Show Context)
Citation Context ...ms as well. We give a geometric construction of the Lie algebras of tangential symmetries associated to the Darboux integrable systems. This construction has the advantage over previous constructions =-=[14, 15]-=-, [12, 13] that our construction does not require the use of adapted coordinates and works for arbitrary dimension of the underlying manifold. In particular it works for the prolongations of decomposa... |

6 |
Duality and Integrable Systems of Pseudoholomorphic Curves
- McKay
- 1999
(Show Context)
Citation Context ...uations was introduced by Gaston Darboux [5, 6]. Generalizations to many other systems are known, such as first order systems [13], hyperbolic exterior differential systems [3] and elliptic equations =-=[10]-=-. An important step in the classification of Darboux integrable equations was given by Vessiot in the papers [14, 15]. Vessiot associates to each second order equation Darboux integrable at order 2 a ... |

3 | Lie’s Structural Approach to PDE Systems, volume 80 of Encyclopedia of Mathematics and its Applications - Stormark - 2000 |

2 | Contact Structures of Partial Differential Equations - Eendebak - 2006 |

1 | Superposition formulas for Darboux integrable exterior differential systems
- Anderson, Fels, et al.
- 2007
(Show Context)
Citation Context ...r arbitrary dimension of the underlying manifold. In particular it works for the prolongations of decomposable exterior differential systems. Independently of the author, Anderson, Fels and Vassiliou =-=[1]-=- have developed a theory similar to the one described in this article. Their method has a more algebraic flavor and uses adapted coframes. Their approach allows the use of symbolic software to calcula... |