Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure

被引：0

作者：

Hu, Xin ^{[1
]}

Casati, Matteo ^{[1
]}

机构：

[1] Ningbo Univ, Sch Math & Stat, Ningbo 315211, Peoples R China

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2024年 / 20卷

基金：

美国国家科学基金会;

关键词：

Hamiltonian structures; quasilinear systems; non-homogeneous operators; POISSON BRACKETS; EQUATIONS; DEFORMATIONS; OPERATORS; SPACES;

D O I：

10.3842/SIGMA.2024.081

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the admissible Hamiltonian operators. We present in detail the examples of two-dimensional, two-components systems of hydrodynamic type and of a real reduction of the 3-waves system.

引用

页数：17

共 28 条

[1] NONLINEAR EVOLUTION EQUATIONS - 2 AND 3 DIMENSIONS [J].

ABLOWITZ, MJ ;

HABERMAN, R .

PHYSICAL REVIEW LETTERS, 1975, 35 (18) :1185-1188

[2] Poisson vertex algebras in the theory of Hamiltonian equations [J].

Barakat, Aliaa ;

De Sole, Alberto ;

Kac, Victor G. .

JAPANESE JOURNAL OF MATHEMATICS, 2009, 4 (02) :141-252

[3] Normal forms of dispersive scalar Poisson brackets with two independent variables [J].

Carlet, Guido ;

Casati, Matteo ;

Shadrin, Sergey .

LETTERS IN MATHEMATICAL PHYSICS, 2018, 108 (10) :2229-2253

[4] Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets [J].

Carlet, Guido ;

Casati, Matteo ;

Shadrin, Sergey .

JOURNAL OF GEOMETRY AND PHYSICS, 2017, 114 :404-419

[5] Bihamiltonian Cohomology of KdV Brackets [J].

Carlet, Guido ;

Posthuma, Hessel ;

Shadrin, Sergey .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2016, 341 (03) :805-819

[6] On Deformations of Multidimensional Poisson Brackets of Hydrodynamic Type [J].

Casati, Matteo .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 335 (02) :851-894

[7] NORMAL FORMS FOR SMOOTH POISSON STRUCTURES [J].

CONN, JF .

ANNALS OF MATHEMATICS, 1985, 121 (03) :565-593

[8]

DUBROVIN BA, 1983, DOKL AKAD NAUK SSSR+, V270, P781

[9]

Dubrovin BA, 2001, ENCYL MATH SCI, V4, P177

[10]

Dubrovin B, 2001, Arxiv, DOI arXiv:math/0108160

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