Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nondegeneracy, Morse Index and Orbital Stability of the Lump Solution to
  the KP-I Equation   Let $Q(x,y)= 4 \frac{y^2-x^2+3}{ (x^2+y^2+3)^2}$ be the lump solution of the
KP-I equation $$ \partial_x^2 (\partial_x^2 u-u + 3 u^2)-\partial_y^2 u=0.$$ We
show that this solution is rigid in the following senses: the only decaying
solutions to the linearized operator $$ \partial_x^2 (\partial_x^2 \phi -\phi +
6 Q \phi)-\partial_y^2 \phi=0$$ consist of the linear combinations of $
\partial_x Q$ and $ \partial_y Q$. Furthermore we show that the Morse index is
exactly one and that it is orbital stable.

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The categories of this paper are: cond-mat
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The categories of this paper are: stat
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
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The categories of this paper are: eess
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an