Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary Value Problem for $r^2 d^2 f/dr^2 + f = f^3$ (II): Connection
  Formula   In this paper, we study the analytic expansion in a small neighborhood of 0
in the complex plane for the solution to the equation $p dp/dz - p =
z(z-1)(z-2)$ satisfying $p(z) = -z + O(z^2)$ as $z \to 0$. We show that the
expansion is valid for $|z| \le s_0$, where $s_0 >1$. Then we get an explicit
formula for $p(1)$ which is used to give the connection formula for the problem
$r^2 f^{''} + f = f^3$, $f(1) = 0, f(\infty) = 1$.

1
The categories of this paper are: cs
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ