Geodesic
SECOND-ORDER DEFORMATIONS OF HYDRODYNAMIC-TYPE POISSON BRACKETS
Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 75-82

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DOI

This 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. 
FERGUSON, JAMES T. SECOND-ORDER DEFORMATIONS OF HYDRODYNAMIC-TYPE POISSON BRACKETS. Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 75-82. doi: 10.1017/S0017089508004795
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     author = {FERGUSON, JAMES T.},
     title = {SECOND-ORDER {DEFORMATIONS} {OF} {HYDRODYNAMIC-TYPE} {POISSON} {BRACKETS}},
     journal = {Glasgow mathematical journal},
     pages = {75--82},
     year = {2009},
     volume = {51},
     number = {A},
     doi = {10.1017/S0017089508004795},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004795/}
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