On commuting differential operators
The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs $(P,L)$. Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the d...
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| Format: | Article |
| Language: | English |
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Texas State University
2000-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2000/19/abstr.html |
| _version_ | 1830209914865188864 |
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| author | R. Weikard |
| author_facet | R. Weikard |
| author_sort | R. Weikard |
| collection | DOAJ |
| description | The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs $(P,L)$. Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations $Ly=zy$, $zin {Bbb C}$, are meromorphic. In this paper this relationship is explored further by establishing its existence for Gelfand-Dikii systems with rational and simply periodic coefficients. |
| first_indexed | 2024-12-18T05:17:45Z |
| format | Article |
| id | doaj.art-9149fb899f1a46b889b0b76a08e83ab5 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T05:17:45Z |
| publishDate | 2000-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-9149fb899f1a46b889b0b76a08e83ab52022-12-21T21:19:44ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912000-03-01200019111On commuting differential operatorsR. WeikardThe theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs $(P,L)$. Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations $Ly=zy$, $zin {Bbb C}$, are meromorphic. In this paper this relationship is explored further by establishing its existence for Gelfand-Dikii systems with rational and simply periodic coefficients.http://ejde.math.txstate.edu/Volumes/2000/19/abstr.htmlMeromorphic solutionsCommuting differential expressionsLax pairsKdVGelfand-Dikii systems. |
| spellingShingle | R. Weikard On commuting differential operators Electronic Journal of Differential Equations Meromorphic solutions Commuting differential expressions Lax pairs KdV Gelfand-Dikii systems. |
| title | On commuting differential operators |
| title_full | On commuting differential operators |
| title_fullStr | On commuting differential operators |
| title_full_unstemmed | On commuting differential operators |
| title_short | On commuting differential operators |
| title_sort | on commuting differential operators |
| topic | Meromorphic solutions Commuting differential expressions Lax pairs KdV Gelfand-Dikii systems. |
| url | http://ejde.math.txstate.edu/Volumes/2000/19/abstr.html |
| work_keys_str_mv | AT rweikard oncommutingdifferentialoperators |