Nonlocal aspects of λ-symmetries and ODEs reduction

2007/02/28 by Diego Catalano Ferraioli · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math-ph #math.DG #math.MP #msc:34C14

paper · pdf · doi:10.1088/1751-8113/40/21/002

13 pages

arxiv created 2007/04/16 · openalex publication_date 2007/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A reduction method of ODEs not possessing Lie point symmetries makes use of the so called λ-symmetries (C. Muriel and J. L. Romero, IMA J. Appl. Math. 66, 111-125, 2001). The notion of covering for an ODE Y is used here to recover λ-symmetries of Y as nonlocal symmetries. In this framework, by embedding Y into a suitable system Y^′ determined by the function λ, any λ-symmetry of Y can be recovered by a local symmetry of Y^′. As a consequence, the reduction method of Muriel and Romero follows from the standard method of reduction by differential invariants applied to Y^′.

Cited by

• Reduction of systems of first-order differential equations via Λ-symmetries
• Local and nonlocal solvable structures in the reduction of ODEs