2024/09/30 by Mark E. Fels, Fels, Mark E., Thomas Ivey +1
Mathematics · Physics and Astronomy · #35A30 #35C60 #35J60 #53A55 #53C15 #53C56 #58A15 #Advanced Differential Equations and Dynamical Systems #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2409.19893
openalex publication_date 2024/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize real elliptic differential systems whose solutions can be expressed in terms of holomorphic solutions to an associated holomorphic Pfaffian system \mathcal H on a complex manifold. In particular, these elliptic systems arise as quotients by a group G of the real differential system generated by the real and imaginary parts of \mathcal H, such that G is the real form of a complex Lie group K which is a symmetry group of \mathcal H. Subject to some mild genericity assumptions, we show that such elliptic systems are characterized by a property known as Darboux integrability. Examples discussed include first- and second-order elliptic PDE and PDE systems in the plane.