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We consider a generalization of nonrelativistic Schr\"odinger-HiggsLagrangian by introducing a nonstandard kinetic term. We show that this modelis Galilean invariant, we construct the conserved charges associated to thesymmetries and realize the algebra of the Galilean group. In addition, we studythe model in the presence of a gauge field. We also show that the gauged modelis Galilean invariant. Finally, we explore relations between twin models andtheir solutions.

Galilean symmetry in generalized abelian Schr\"odinger-Higgs models with and without gauge field interaction