Premium
A relationship between λ ‐symmetries and first integrals for ordinary differential equations
Author(s) -
Zhang Jin
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5711
Subject(s) - mathematics , homogeneous space , ordinary differential equation , integrating factor , pure mathematics , differential operator , representation (politics) , mathematical analysis , differential equation , mathematical physics , algebra over a field , differential algebraic equation , geometry , politics , political science , law
In this paper, we provide some geometric properties of λ ‐symmetries of ordinary differential equations using vector fields and differential forms. According to the corresponding geometric representation of λ ‐symmetries, we conclude that first integrals can also be derived if the equations do not possess enough symmetries. We also investigate the properties of λ ‐symmetries in the sense of the deformed Lie derivative and differential operator. We show that λ ‐symmetries have the exact analogous properties as standard symmetries if we take into consideration the deformed cases.