Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Loss of Compactness in the Vectorial Heteroclinic Connection
  Problem   We give an alternative proof of the theorem of Alikakos-Fusco [AF] concerning
existence of heteroclinic solutions to a Hamiltonian ODE system on the whole
real line which arises in the theory of phase transitions. Our method is
variational but differs from the original artificial constraint method of [AF]
and establishes existence by analysing the loss of compactness in minimising
sequences of the action in the appropriate functional space. Our assumptions
are slightly different from those considered previously and also imply a priori
estimates for the solution.

33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol