Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom   We study the variable bottom generalized Korteweg-de Vries (bKdV) equation dt
u=-dx(dx^2 u+f(u)-b(t,x)u), where f is a nonlinearity and b is a small, bounded
and slowly varying function related to the varying depth of a channel of water.
Many variable coefficient KdV-type equations, including the variable
coefficient, variable bottom KdV equation, can be rescaled into the bKdV. We
study the long time behaviour of solutions with initial conditions close to a
stable, b=0 solitary wave. We prove that for long time intervals, such
solutions have the form of the solitary wave, whose centre and scale evolve
according to a certain dynamical law involving the function b(t,x), plus an
H^1-small fluctuation.

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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex