Geodesic
Conservation laws of zero order for one-dimensional rotating shallow water equations
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 1, pp. 59-70

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All conservation laws of the one-dimensional rotating shallow water equations are found. The Casimir functional with differentiation of any order for the Poisson bracket of the one-dimensional baroclinic fluid is constructed. 
@article{VNGU_2008_8_1_a5,
     author = {S. B. Medvedev},
     title = {Conservation laws of zero order for one-dimensional rotating shallow water equations},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {59--70},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2008_8_1_a5/}
}
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S. B. Medvedev. Conservation laws of zero order for one-dimensional rotating shallow water equations. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 1, pp. 59-70. http://geodesic.mathdoc.fr/item/VNGU_2008_8_1_a5/