On some generalizations of the factorization method

First Integrals Generated by Pseudosymmetries in Nambu-Poisson Mechanics

“…where α, β, γ, δ ∈ C, β = 0, reduces to linear equations with variable coefficients by the generalized factorization method [7]. As usual, the operation * is defined by the formula (3.9).…”

“…We believe that the concrete systems that appear in Section 2 as examples could be used for examining some of the conjectures in the literature about singularity analysis. It would be interesting also to investigate which types of singularities are possible for systems integrable by the generalized factorization method [7].…”

“…Some generalizations of non-associative algebras such as Lie, leftsymmetric and Jordan algebras naturally arise there. In Section 5 we show that, besides (1.7), the factorization method can be applied to the following equation 8) where c i ∈ C. In a particular case when * is a Lie operation, (1.8) has been linearized in [7]. Moreover, equations (1.7) (see [7]) and (1.8) can be reduced to linear equations with variable coefficients in the following more general case.…”

“…In Section 5 we show that, besides (1.7), the factorization method can be applied to the following equation 8) where c i ∈ C. In a particular case when * is a Lie operation, (1.8) has been linearized in [7]. Moreover, equations (1.7) (see [7]) and (1.8) can be reduced to linear equations with variable coefficients in the following more general case. Let (1.2) be a vector space decomposition, where G + and G − are not subalgebras as before, but vector spaces satisfying the following conditions…”

Properties of the Dominant Behaviour of Quadratic Systems

“…These analyses have been devoted to systems of the type (1.1). Golubchik and Sokolov [12,13] introduced a class of integrable quadratic systems in the context of the YangBaxter equations and Cotsakis et al [16] analysed exemplars of this class in terms of their singularity and symmetry properties.…”