Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collective coordinate approximation to the scattering of solitons in
  modified NLS and sine-Gordon models   We investigate the validity of collective coordinate approaximations to the
scattering of solitons in several classes of models in (1+1) dimensional field
theory models. We look at models which are deformations of the sine-Gordon (SG)
or the nonlinear Schr\"odinger (NLS) model as they posses solitons which are
topological (SG) or non-topological (NLS). Our deformations preserve their
topology (SG), but changes their integrability properties, either completely or
partially (models become `quasi-integrable').
  As our collective coordinate approximation does not allow for the radiation
of energy out the system we look also, in some detail, at how good this
approximation is for models which are `quasi-integrable'. Our results are based
on the studies of the interactions and scatterings in two soliton systems.
  Our results show that a well chosen approximation, based on geodesic motion
etc, works amazingly well in all cases where it is expected to work. This is
true for the trajectories of the solitons and even for their quasi-conserved
(or not) charges. The only time the approximation is not very reliable (and
even then the qualitative features are reasonable, but some details are not
reproduced well) involves the processes when the solitons, during their
scattering, can come very close together (within one width of each other).

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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: math
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The categories of this paper are: solv-int