On a class of third-order nonlocal Hamiltonian operators

被引：6

作者：

Casati, M. ^{[1
]}

Ferapontov, E. V. ^{[1
]}

Pavlov, M. V. ^{[2
]}

Vitolo, R. F. ^{[3
,4
]}

机构：

[1] Loughborough Univ, Dept Math Sci, Loughborough LE11 3TU, Leics, England

[2] Russian Acad Sci, Lebedev Phys Inst, Sect Math Phys, Leninskij Prospekt 53, Moscow, Russia

[3] Univ Salento, Dept Math & Phys E De Giorgi, Lecce, Italy

[4] Ist Nazl Fis Nucl, Sect Lecce, Lecce, Italy

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2019年 / 138卷

关键词：

Nonlocal Hamiltonian operator; Monge metric; Dirac reduction; Poisson vertex algebra; POISSON STRUCTURES; EQUATIONS; ASSOCIATIVITY; BRACKETS;

D O I：

10.1016/j.geomphys.2018.10.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on the theory of Poisson vertex algebras we calculate skew-symmetry conditions and Jacobi identities for a class of third-order nonlocal operators of differential-geometric type. Hamiltonian operators within this class are defined by a Monge metric and a skew-symmetric two-form satisfying a number of differential-geometric constraints. Complete classification results in the 2-component and 3-component cases are obtained. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：285 / 296

页数：12

共 50 条

[31] One Class of Third-Order Linear ODE's
Slavyanov, S. Yu.
COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING, 2010, 6244 : 232 - 237
[32] Analytic properties of solutions of a class of third-order equations
T. K. Andreeva
I. P. Martynov
V. A. Pron’ko
Differential Equations, 2011, 47 : 1231 - 1236
[33] PROPERTIES OF SOLUTIONS OF A CLASS OF THIRD-ORDER DIFFERENTIAL EQUATIONS
JONES, GD
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 48 (01) : 165 - 169
[34] VERIFICATION OF AIZERMANS CONJECTURE FOR A CLASS OF THIRD-ORDER SYSTEMS
BERGEN, AR
WILLIAMS, IJ
IRE TRANSACTIONS ON AUTOMATIC CONTROL, 1962, AC 7 (03): : 42 - &
[35] LIMIT CYCLES FOR A CLASS OF THIRD-ORDER DIFFERENTIAL EQUATIONS
Llibre, Jaume
Yu, Jiang
Zhang, Xiang
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2010, 40 (02) : 581 - 594
[36] EULER CASE FOR A CLASS OF THIRD-ORDER DIFFERENTIAL EQUATION
Al-Hammadi, A. S. A.
MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2010, 51 : 5 - 15
[37] On the Solvability of One Class of Third-Order Differential Equations
Bilalov, B. T.
Ismailov, M. I.
Kasumov, Z. A.
UKRAINIAN MATHEMATICAL JOURNAL, 2021, 73 (03) : 367 - 383
[38] On first integrals of a class of third-order differential equations
N. S. Berezkina
I. P. Martynov
V. A. Pron’ko
Differential Equations, 2009, 45 : 1536 - 1538
[39] A class of Newton's methods with third-order convergence
Zhou Xiaojian
APPLIED MATHEMATICS LETTERS, 2007, 20 (09) : 1026 - 1030
[40] SELF-ADJOINT REALIZATION OF A CLASS OF THIRD-ORDER DIFFERENTIAL OPERATORS WITH AN EIGENPARAMETER CONTAINED IN THE BOUNDARY CONDITIONS
Li, Kun
Bai, Yulin
Wang, Wanyi
Meng, Fanwei
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2020, 10 (06): : 2631 - 2643

← 1 2 3 4 5 →