Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations

Abelian Lie symmetry algebras of two‐dimensional quasilinear evolution equations

“…Definition The (usual) equivalence group of the class is the (pseudo)group of point transformations in the space of which are projectable to the space of for any , are consistent with the contact structure on the space of , and preserve the class 19 …”

“…The (usual) equivalence group G ∼ = G ∼ () of the class  is the (pseudo)group of point transformations in the space of (x, u (r) , 𝜃) which are projectable to the space of (x, u (r′) ) for any 0 ≤ r ′ ≤ r, are consistent with the contact structure on the space of (x, u (r) ), and preserve the class . 19 Definition 2. The class of differential equations  is called normalized if its equivalence groupoid  ∼ is induced by its equivalence group G ∼ , meaning that for any triple (𝜃, 𝜉, θ) from  ∼ , there exists a transformation Ξ from G ∼ such that θ = Ξ * 𝜃 and 𝜉 = Ξ| (x,u) .…”