Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The geodesic approximation for lump dynamics and coercivity of the
  Hessian for harmonic maps   The most fruitful approach to studying low energy soliton dynamics in field
theories of Bogomol'nyi type is the geodesic approximation of Manton. In the
case of vortices and monopoles, Stuart has obtained rigorous estimates of the
errors in this approximation, and hence proved that it is valid in the low
speed regime. His method employs energy estimates which rely on a key
coercivity property of the Hessian of the energy functional of the theory under
consideration. In this paper we prove an analogous coercivity property for the
Hessian of the energy functional of a general sigma model with compact K\"ahler
domain and target. We go on to prove a continuity property for our result, and
show that, for the CP^1 model on S^2, the Hessian fails to be globally coercive
in the degree 1 sector. We present numerical evidence which suggests that the
Hessian is globally coercive in a certain equivariance class of the degree n
sector for n>1. We also prove that, within the geodesic approximation, a single
CP^1 lump moving on S^2 does not generically travel on a great circle.

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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int