In this contribution we review and summarize recent articles on a family of nonlinear Schrödinger equations proposed by G.A. Goldin and one of us (HDD) [J.Phys. A. 27, 1994, 1771-1780], dealing with a gauge description of the family, a classification of its Lie symmetries in terms of gauge invariants and the integrability of certain sub-families indicated by their Lie symmetry, respectively.
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Nattermann et al. (1996) studied this question.
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