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On preliminary symmetry classification of nonlinear Schrödinger equations with some applications to Doebner-Goldin models. (English) Zbl 0970.81024
Summary: We perform classification of a class of one-dimensional nonlinear Schrödinger equations whose symmetry groups have dimensions $n=1,2, 3$. Next, from so constructed classes of invariant equations we select those nonlinear Schrödinger equations which are invariant with respect to the Galilei group and its natural extensions. The results obtained are applied for the symmetry classification of complex Galilei-invariant Doebner-Goldin models.

81R05Representations of finite-dimensional groups and algebras in quantum theory
81Q05Closed and approximate solutions to quantum-mechanical equations
35Q55NLS-like (nonlinear Schrödinger) equations
58J70Invariance and symmetry properties
Full Text: DOI
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