Geodesic
Compatible Poisson brackets for Lax equations and classical $r$-matrices
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part IX, Tome 164 (1987), pp. 176-188

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For Lax equations and zero curvature equations with spectral parameter a family of compatible linear Poisson brackets is constructed. 
@article{ZNSL_1987_164_a13,
     author = {A. G. Reiman and M. A. Semenov-Tian-Shansky},
     title = {Compatible {Poisson} brackets for {Lax} equations and classical $r$-matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {176--188},
     publisher = {mathdoc},
     volume = {164},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_164_a13/}
}
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A. G. Reiman; M. A. Semenov-Tian-Shansky. Compatible Poisson brackets for Lax equations and classical $r$-matrices. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part IX, Tome 164 (1987), pp. 176-188. http://geodesic.mathdoc.fr/item/ZNSL_1987_164_a13/