2008/07/31 by Diego Catalano Ferraioli, Paola Morando · 37 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Applied mathematics #Differential equation #Geometry #Homogeneous space #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations #Ode #Ordinary differential equation #Pure mathematics #Reduction (mathematics) #Scalar (mathematics) #Symmetry (geometry) #math-ph #math.DG #math.MP #msc:34C14 #msc:70S10
paper · pdf · doi:10.1088/1751-8113/42/3/035210
published in Journal of Physics A Mathematical and Theoretical 42(3), 035210 (Institute of Physics)
arxiv created 2008/11/27 · openalex publication_date 2008/12/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ordinary differential equations (ODEs) by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable structures even though finding them in general could be a very difficult task. In practice, a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra. In this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order (i.e., classical and higher). In particular we introduce the notion of nonlocal solvable structure.