 0599 S. I. Dejak, B. L. G. Jonsson
 LongTime Dynamics of Variable Coefficient mKdV Solitary Waves
(75K, LATeX 2e)
Mar 8, 05

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Abstract. We study the Kortewegde Vriestype equation dt
u=dx(dx^2 u+f(u)B(t,x)u), where B is a small and
bounded, slowly varying function and f is a nonlinearity. Many
variable coefficient KdVtype equations can be rescaled into this
equation. 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^1small fluctuation.
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