2010/10/31 by Ekaterina Shemyakova
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic differential equation #Darboux integral #Differential algebraic equation #Differential equation #Differential operator #Geometry #Laplace transform #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Operator (biology) #Ordinary differential equation #Partial differential equation #Plane (geometry) #Polynomial and algebraic computation #Pure mathematics #Transformation (genetics) #math-ph #math.AP #math.MP
paper · pdf · doi:10.1134/s0361768811020095
published as Programming and Computer Software, MAIK Nauka/Interperiodica, 192--196, Vol.37, issue 4, 2011
openalex publication_date 2011/07/01 · arxiv created 2011/08/19 · arxiv updated 2011/08/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In the paper, a classical computer algebra problem—symbolic solution of differential equations—is considered. Particularly, widely used Darboux theorems on transformation of hyperbolic operators in the plane are extended to the space of invariants by means of differential substitutions. X - and Y -invariants for such operators are introduced as solutions of some equations written in terms of the Laplace invariants of operator L with respect to gauge transformations. Explicit formulas of transformations of sets of X - and Y -invariants under the Darboux transformations are obtained.