Let G be a connected reductive complex algebraic group with maximal torus T. We denote by Λ the coweight lattice of Λ+⊂Λ submonoid dominant coweights. For λ∈Λ+,μ∈Λ,μ⩽λ, in [7], authors defined generalized transversal slice W‾μλ. This is an variety dimension 〈2ρ∨,λ−μ〉, where 2ρ∨ sum positive roots G. In this paper, we construct isomorphism W‾μλ≃W‾μ+λ×A〈2ρ∨,μ+−μ〉 for μ∈Λ such that 〈α∨,μ〉⩾−1 any r...

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The goal of this paper is to calculate of order reduction of the KdV typeequation and the non-isospectral KdV type equation using the μ-symmetrymethod. Moreover we obtain μ-conservation law of the non-isospectral KdVtype equation using the variational problem method.