Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Special polynomials and soliton dynamics   Special polynomials play a role in several aspects of soliton dynamics. These
are differential polynomials in u, the solution of a nonlinear evolution
equation, which vanish identically when u represents a single soliton. Local
special polynomials contain only powers of u and its spatial derivatives.
Non-local special polynomials contain, in addition, non-local entities (e.g.,
\delta x-1u). When u is a multiple-solitons solution, local special polynomials
are localized in the vicinity of the soliton-collision region and fall off
exponentially in all directions away from this region. Non-local ones are
localized along soliton trajectories.
  Examples are presented of how, with the aid of local special polynomials, one
can modify equations that have only a single-soliton solution into ones, which
have that solution as well as, at least, a two-solitons solutions.
  Given an integrable equation, with the aid of local special polynomials, it
is possible to find all evolution equations in higher scaling weights, which
share the same single-soliton solution and are either integrable, or, at least,
have a two-solitons solution. This is demonstrated for one or two consecutive
scaling weights for a number of known equations.
  In the study of perturbed integrable equations, local special polynomials are
responsible for inelastic soliton interactions generated by the perturbation in
the multiple-soliton case, and for the (possible) loss of asymptotic
integrability. Non-local special polynomials describe higher-order corrections
to the solution, which are of an inelastic nature.

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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat