Two remarks on the generalised Korteweg de-Vries equation
| dc.creator | Tao, Terence | |
| dc.date | 2006-06-09 | |
| dc.date | 2009-01-20 | |
| dc.date.accessioned | 2026-07-07T12:31:42Z | |
| dc.date.available | 2026-07-07T12:31:42Z | |
| dc.description | We make two observations concerning the generalised Korteweg de Vries equation $u_t + u_{xxx} = μ(|u|^{p-1} u)_x$. Firstly we give a scaling argument that shows, roughly speaking, that any quantitative scattering result for $L^2$-critical equation ($p=5$) automatically implies an analogous scattering result for the $L^2$-critical nonlinear Schrödinger equation $iu_t + u_{xx} = μ|u|^4 u$. Secondly, in the defocusing case $μ> 0$ we present a new dispersion estimate which asserts, roughly speaking, that energy moves to the left faster than the mass, and hence strongly localised soliton-like behaviour at a fixed scale cannot persist for arbitrarily long times. | |
| dc.description | 16 pages, no figures. A footnote is corrected | |
| dc.identifier | https://arxiv.org/abs/math/0606236 | |
| dc.identifier | http://arxiv.org/abs/math/0606236 | |
| dc.identifier | Discrete Cont. Dynam. Systems 18 (2007), 1-14 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216533 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q53 | |
| dc.title | Two remarks on the generalised Korteweg de-Vries equation | |
| dc.type | text |