Reducing triangular systems of ODEs with rational coefficients, with\n applications to coupled Regge-Wheeler equations

2018/01/29 by Igor Khavkine, Khavkine, Igor
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1801.09800

openalex publication_date 2018/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We concisely summarize a method of finding all rational solutions to an\ninhomogeneous rational ODE system of arbitrary order (but solvable for its\nhighest order terms) by converting it into a finite dimensional linear algebra\nproblem. This method is then used to solve the problem of conclusively deciding\nwhen certain rational ODE systems in upper triangular form can or cannot be\nreduced to diagonal form by differential operators with rational coefficients.\nAs specific examples, we consider systems of coupled Regge-Wheeler equations,\nwhich have naturally appeared in previous work on vector and tensor\nperturbations on the Schwarzschild black hole spacetime. Our systematic\napproach reproduces and complements identities that have been previously found\nby trial and error methods.\n

Related

• Rational Solutions of Parametric First-Order Algebraic Differential Equations
• Triangular Schlesinger systems and superelliptic curves
• Algebraic, rational and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one
• The rational generalized integrating factors for first-order ODEs
• Systèmes aux q-différences singuliers réguliers: solutions canoniques, classification, matrice de connexion et monodromie