Darboux Polynomials, Balances and Painleve Property

被引：1

作者：

Llibre, Jaume ^{[1
]}

Valls, Claudia ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

[2] Univ Lisbon, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon, Portugal

来源：

REGULAR & CHAOTIC DYNAMICS | 2017年 / 22卷 / 05期

关键词：

Painleve property; Darboux polynomial; Kovalevskaya exponents; ALGEBRAIC 1ST INTEGRALS; KOWALEVSKI EXPONENTS; EXISTENCE; SYSTEMS;

D O I：

10.1134/S1560354717050057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of the system and the Painleve property. As far as we know, these are the first results which relate the Darboux theory of integrability, first, to the Painleve property and, second, to the Kovalevskaya exponents. The relation of these last two notions to the general integrability has been intensively studied over these last years.

引用

页码：543 / 550

页数：8

共 50 条

[21] On the Umemura polynomials for the Painleve III equation
Kajiwara, K
Masuda, T
PHYSICS LETTERS A, 1999, 260 (06) : 462 - 467
[22] Umemura polynomials for the Painleve V equation
Noumi, M
Yamada, Y
PHYSICS LETTERS A, 1998, 247 (1-2) : 65 - 69
[23] Special polynomials and generalized Painleve equations
Yamada, Y
COMBINATORIAL METHODS IN REPRESENTATION THEORY, 2000, 28 : 391 - 400
[24] Liouvillian Integrability Versus Darboux Polynomials
Llibre, Jaume
Valls, Claudia
Zhang, Xiang
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2016, 15 (02) : 503 - 515
[25] Monomial Derivations without Darboux Polynomials
Li Jian-tao
Communications in Mathematical Research, 2017, 33 (02) : 185 - 192
[26] On the Painleve property of a hydrodynamic system
Noshchenko, Dmitry
Perezhogin, Andrey
VII INTERNATIONAL CONFERENCE "SOLAR-TERRESTRIAL RELATIONS AND PHYSICS OF EARTHQUAKES PRECURSORS", 2016, 11
[27] KdV extensions with painleve property
Lou, SY
JOURNAL OF MATHEMATICAL PHYSICS, 1998, 39 (04) : 2112 - 2121
[28] Automated Reasoning For The Existence Of Darboux Polynomials
Ghorbal, Khalil
Bridoux, Maxime
PROCEEDINGS OF THE 2024 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2024, 2024, : 324 - 333
[29] BACKLUND TRANSFORMATION AND THE PAINLEVE PROPERTY
WEISS, J
JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (05) : 1293 - 1305
[30] Exceptional orthogonal polynomials and the Darboux transformation
Gomez-Ullate, D.
Kamran, N.
Milson, R.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (43)

← 1 2 3 4 5 →