05-99 S. I. Dejak, B. L. G. Jonsson
Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves (75K, LATeX 2e) Mar 8, 05
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 05-99.tex