Geodesic
Field-theory models that admit alternative Lagrangian formulations.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 121-131

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Some theorems are proved concerning the structure of Lagrangian systems of differential equations for which the Lagrangian is not uniquely determined. In particular, a complete description is obtained for bi-Lagrangian systems of second order with hyperregular Lagrangians quadratic in the derivatives. 
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     author = {F. A. Lunev},
     title = {Field-theory models that admit alternative {Lagrangian} {formulations.~I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {121--131},
     publisher = {mathdoc},
     volume = {89},
     number = {1},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a10/}
}
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F. A. Lunev. Field-theory models that admit alternative Lagrangian formulations.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 121-131. http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a10/