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Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves

S. I. Dejak·B. L. G. Jonsson
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Abstract

We study the Korteweg-de Vries-type 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 KdV-type 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^1-small fluctuation.

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S. I. Dejak, B. L. G. Jonsson. 2005-03-08. Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves. https://doi.org/10.1063/1.2217809

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