Kappeler, Thomas; Schaad, Beat; Topalov, Peter (2013). Qualitative Features of Periodic Solutions of KdV. Communications in Partial Differential Equations, 38(9):1626-1673.
In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space HN, N ≥ 0, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree.
In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space HN, N ≥ 0, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree.
| 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 > Analysis
Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | 9 August 2013 |
| Deposited On: | 06 Dec 2013 11:46 |
| Last Modified: | 24 Jan 2022 02:13 |
| Publisher: | Taylor & Francis |
| ISSN: | 0360-5302 |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1080/03605302.2013.814141 |
Kappeler, Thomas