Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Big Solitons in a Competitive Power Nonlinear Schr\"odinger
  Equation   By introducing and solving two correlative constrained variational problems
as well as spectrum analysis, an approach to fix soliton frequency from the
prescribed mass for nonlinear Schr\"odinger equations is found, and an open
problem in normalized solutions is answered. Then existence and orbital
stability of big solitons depending on frequencies for nonlinear Schr\"odinger
equation with competitive power nonlinearity is proved for the first time. In
addition multi-solitons of the equation with different speeds are constructed
by stable big solitons.

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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int