Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves
Dejak, S. I. ; Jonsson, B. L. G.
arXiv, 0503016 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-03-08
Classification:  Mathematical Physics,  35Q53,  35K40 
@article{0503016,
     author = {Dejak, S. I. and Jonsson, B. L. G.},
     title = {Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0503016}
}

Dejak, S. I.; Jonsson, B. L. G. Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0503016/