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Integrability of Equations Admitting the Nonsolvable Symmetry Algebra so (3,R)
Author(s) -
Muriel C.,
Romero J. L.
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00227
Subject(s) - homogeneous space , mathematics , ordinary differential equation , symmetry (geometry) , order (exchange) , differential equation , partial differential equation , algebra over a field , pure mathematics , mathematical physics , mathematical analysis , geometry , finance , economics
If an ordinary differential equation admits the nonsolvable Lie algebra , and we use any of its generators to reduce the order, the reduced equation does not inherit the remaining symmetries. We prove here how the lost symmetries can be recovered as C ∞ ‐symmetries of the reduced equation. If the order of the last reduced equation is higher than one, these C ∞ ‐symmetries can be used to obtain new order reductions. As a consequence, a classification of the third‐order equations that admit as symmetry algebra is given and a step‐by‐step method to solve the equations is presented.