A New Scheme of Integrability for (bi)Hamiltonian PDE

被引：13

作者：

De Sole, Alberto ^{[1
]}

Kac, Victor G. ^{[2
]}

Valeri, Daniele ^{[3
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Matemat, Ple Aldo Moro 2, I-00185 Rome, Italy

[2] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[3] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2016年 / 347卷 / 02期

基金：

美国国家科学基金会;

关键词：

POISSON VERTEX ALGEBRAS; CLASSICAL W-ALGEBRAS; HIERARCHY;

D O I：

10.1007/s00220-016-2684-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

引用

页码：449 / 488

页数：40

共 21 条

[1] ADLER M, 1979, INVENT MATH, V50, P219
[2] [Anonymous], ARXIVMATH0108160MATH
[3] Poisson vertex algebras in the theory of Hamiltonian equations
Barakat, Aliaa
De Sole, Alberto
Kac, Victor G.
[J]. JAPANESE JOURNAL OF MATHEMATICS, 2009, 4 (02): : 141 - 252
[4] De Sole A., 2016, COMMUN MATH IN PRESS
[5] Adler-Gelfand-Dickey Approach to Classical W-Algebras Within the Theory of Poisson Vertex Algebras
De Sole, Alberto
Kac, Victor G.
Valeri, Daniele
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (21) : 11186 - 11235
[6] Double Poisson vertex algebras and non-commutative Hamiltonian equations
De Sole, Alberto
Kac, Victor G.
Valeri, Daniele
[J]. ADVANCES IN MATHEMATICS, 2015, 281 : 1025 - 1099
[7] Dirac Reduction for Poisson Vertex Algebras
De Sole, Alberto
Kac, Victor G.
Valeri, Daniele
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 331 (03) : 1155 - 1190
[8] Non-local Poisson structures and applications to the theory of integrable systems
De Sole, Alberto
Kac, Victor G.
[J]. JAPANESE JOURNAL OF MATHEMATICS, 2013, 8 (02): : 233 - 347
[9] De Sole A, 2013, COMMUN MATH PHYS, V323, P663, DOI 10.1007/s00220-013-1785-z
[10] Dickey L.A, 2003, SOLITON EQUATIONS HA, V26, DOI DOI 10.1142/ASMP

← 1 2 3 →