Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness of standing-waves for a non-linear Schr\"odinger equation
  with three pure-power combinations in dimension one   We show that symmetric and positive profiles of ground-state standing-wave of
the non-linear Schr\"odinger equation are non-degenerate and unique up to a
translation of the argument and multiplication by complex numbers in the unit
sphere. The non-linear term is a combination of two or three pure-powers. The
class of non-linearities satisfying the mentioned properties can be extended
beyond two or three power combinations. Specifically, it is sufficient that an
Euler differential inequality is satisfied and that a certain auxiliary
function is such that the first local maximum is also an absolute maximum.

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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: stat