Cohen, A; Kappeler, T (1987). The asymptotic behavior of solutions of the Korteweg-de Vries equation evolving from very irregular data. Annals of Physics, 178(1):144-185.
Let u(x, t) be a solution of KdV constructed by the inverse scattering method with u(x, 0) = μ(x), a measure. Under general conditions on μ, there is a pure n-soliton solution of KdV, us(x, t), such that u(x, t) − us(x, t) = O(t−1/3) as t → ∞ uniformly in any [x0, + ∞). If n = 0, then the convergence rate is O(t−2/3) rather than O(t−1/3).
Let u(x, t) be a solution of KdV constructed by the inverse scattering method with u(x, 0) = μ(x), a measure. Under general conditions on μ, there is a pure n-soliton solution of KdV, us(x, t), such that u(x, t) − us(x, t) = O(t−1/3) as t → ∞ uniformly in any [x0, + ∞). If n = 0, then the convergence rate is O(t−2/3) rather than O(t−1/3).
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Physics and Astronomy |
| Language: | English |
| Date: | 1987 |
| Deposited On: | 21 Oct 2009 10:58 |
| Last Modified: | 23 Jan 2022 14:50 |
| Publisher: | Elsevier |
| ISSN: | 0003-4916 |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1016/S0003-4916(87)80016-7 |
Cohen, A