Multidimensional nonlinear Schrodinger equations with exponentially confined solutions

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Abstract
The author studies a class of nonlinear equations that reduce to the Schrodinger equation when a logarithmic term is omitted. They have three interesting features: (a) in their multiparticle form, one can separate the centre-of-mass motion as in the linear case; (b) for a large part of the class, there exist exponentially confined solutions which propagate without deformation; (c) if phi is a solution, and C a constant, then C phi is a solution. Other mechanical properties are briefly surveyed.

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