Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonuniqueness and nonlinear instability of Gaussons under repulsive
  harmonic potential   We consider the Schr{\"o}dinger equation with a nondispersive logarithmic
nonlinearity and a repulsive harmonic potential. For a suitable range of the
coefficients, there exist two positive stationary solutions, each one
generating a continuous family of solitary waves. These solutions are Gaussian,
and turn out to be orbitally unstable. We also discuss the notion of ground
state in this setting: for any natural definition, the set of ground states is
empty.

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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: econ