Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic stability of sharp fronts. I One bound state implies
  stability   We study the asymptotic stability of the traveling front solutions to
nonlinear dispersive equations of Burgers type. Our main example is the
Korteweg-de Vries-Burgers (KdVB) equation although the result holds much more
generally. Exploiting a modulation of the translation parameter and making an
energy estimate we establish our stability criterion that a Schr\"odinger
equation in one dimension have exactly one negative eigenvalue so that a
rank-one perturbation of the operator can be made positive semi-definite.
Counting the number of bound states of the Schr\"odinger equation in one
dimension, we find a sufficient condition for stability in terms of Bargmann's
integral, which can be interpreted as the distance between the monotonization
of the front and a corresponding ideal shock. For the KdVB equation we
analytically verify that our stability criterion is met in an open interval of
the relative dispersion parameter which includes all monotone fronts. Numerical
experiments suggest stability for a larger interval.

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The categories of this paper are: dg-ga
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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: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th