Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom
| dc.creator | Dejak, S. I. | |
| dc.creator | Sigal, I. M. | |
| dc.date | 2004-11-17 | |
| dc.date.accessioned | 2026-07-07T04:31:38Z | |
| dc.date.available | 2026-07-07T04:31:38Z | |
| dc.description | 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. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0411059 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0411059 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57891 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q53; 37K40; 35Q35 | |
| dc.title | Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom | |
| dc.type | text |