ON COMMUTING DIFFERENTIAL OPERATORS

被引：0

作者：

Weikard, R. ^{[1
]}

机构：

[1] Univ Alabama Birmingham, Dept Math, Birmingham, AL 35294 USA

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2000年

关键词：

Meromorphic solutions; Commuting differential expressions; Lax pairs; KdV; Gelfand-Dikii systems;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, z is an element of 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.

引用

页数：11

共 50 条

[21] Bispectral Algebras of Commuting Ordinary Differential Operators
B. Bakalov
E. Horozov
M. Yakimov
[J]. Communications in Mathematical Physics, 1997, 190 : 331 - 373
[22] COMMUTING DIFFERENTIAL OPERATORS IN TWO-DIMENSION
Shabat, A. B.
Elkanova, Z. S.
[J]. UFA MATHEMATICAL JOURNAL, 2011, 3 (02): : 89 - 95
[23] Quantum tops as examples of commuting differential operators
V. E. Adler
V. G. Marikhin
A. B. Shabat
[J]. Theoretical and Mathematical Physics, 2012, 172 : 1187 - 1205
[24] SIMPLIFIED SCHLESINGER SYSTEMS AND ALGEBRAS OF COMMUTING DIFFERENTIAL OPERATORS
CHUDNOVSKY, DV
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1979, 289 (08): : 459 - 462
[25] Commuting Differential Operators of Rank 2 with Rational Coefficients
V. S. Oganesyan
[J]. Functional Analysis and Its Applications, 2018, 52 : 203 - 213
[26] Common eigenfunctions of commuting differential operators of rank 2
V. S. Oganesyan
[J]. Mathematical Notes, 2016, 99 : 308 - 311
[27] Common eigenfunctions of commuting differential operators of rank 2
Oganesyan, V. S.
[J]. MATHEMATICAL NOTES, 2016, 99 (1-2) : 308 - 311
[28] Commuting Differential Operators of Rank 2 with Rational Coefficients
Oganesyan, V. S.
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2018, 52 (03) : 203 - 213
[29] Self-adjoint commuting ordinary differential operators
Andrey E. Mironov
[J]. Inventiones mathematicae, 2014, 197 : 417 - 431
[30] Commuting Differential Operators of Rank 2 with Polynomial Coefficients
V. S. Oganesyan
[J]. Functional Analysis and Its Applications, 2016, 50 : 54 - 61

← 1 2 3 4 5 →