Form-invariant Poisson brackets of hydrodynamic type with several spatial variables

2008 ◽  
Vol 49 (5) ◽  
pp. 053520 ◽  
Author(s):  
O. Bogoyavlenskij ◽  
P. Reynolds
Keyword(s):  
Hydrodynamic Type ◽  
Poisson Brackets ◽  
Spatial Variables

On the central extensions of Poisson brackets of hydrodynamic type

2003 ◽  
Vol 36 (9) ◽  
pp. 2261-2269
Author(s):  
Chengming Bai ◽  
Daoji Meng ◽  
Hongbiao Zhang
Keyword(s):  
Hydrodynamic Type ◽  
Poisson Brackets ◽  
Central Extensions

scholarly journals SECOND-ORDER DEFORMATIONS OF HYDRODYNAMIC-TYPE POISSON BRACKETS

2009 ◽  
Vol 51 (A) ◽  
pp. 75-82
Author(s):  
JAMES T. FERGUSON
Keyword(s):  
Differential Operator ◽  
Poisson Bracket ◽  
Hamiltonian Structure ◽  
Second Order ◽  
Hydrodynamic Type ◽  
Poisson Brackets ◽  
Geometric Type

AbstractThis paper is concerned with the properties of differential-geometric-type Poisson brackets specified by a differential operator of degree 2. It also considers the conditions required for such a Poisson bracket to form a bi-Hamiltonian structure with a hydrodynamic-type Poisson bracket.

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