Normal forms of dispersive scalar Poisson brackets with two independent variables

被引：2

作者：

Carlet, Guido ^{[1
]}

Casati, Matteo ^{[2
,3
]}

Shadrin, Sergey ^{[4
]}

机构：

[1] Univ Bourgogne Franche Compte, CNRS, UMR 5584, IMB, F-21000 Dijon, France

[2] Ist Nazl Alta Matemat, Rome, Italy

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

[4] Univ Amsterdam, Korteweg de Vries Inst Wiskunde, Postbus 94248, NL-1090 GE Amsterdam, Netherlands

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2018年 / 108卷 / 10期

关键词：

Poisson brackets; Poisson cohomology; Hamiltonian operator; Miura transformation; DUBROVIN-NOVIKOV BRACKETS; HYDRODYNAMIC TYPE; HAMILTONIAN OPERATORS; DEFORMATIONS; HIERARCHIES; COHOMOLOGY; MANIFOLDS; SYSTEMS; THEOREM;

D O I：

10.1007/s11005-018-1076-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well-known triviality result exists, the Miura equivalence classes are parametrised by an infinite number of constants, which we call numerical invariants of the brackets. We obtain explicit formulas for the first few numerical invariants.

引用

页码：2229 / 2253

页数：25

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