Geodesic
Helmholtz potentiality conditions for systems of difference-differential equations
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 437-442

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For operators corresponding to systems of $\mu$th-order difference-differential equations of neutral type, necessary and sufficient conditions for potentiality with respect to the classical bilinear form are obtained. These results are applied to first-order quasilinear systems. 
@article{MZM_1998_64_3_a12,
     author = {A. M. Popov},
     title = {Helmholtz potentiality conditions for systems of difference-differential equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {437--442},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a12/}
}
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A. M. Popov. Helmholtz potentiality conditions for systems of difference-differential equations. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 437-442. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a12/