Geodesic
An~effective algorithm for finding multidimensional conservation laws for integrable systems of hydrodynamic type
Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 2, pp. 320-330

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We study a new property of integrable systems, the existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional hydrodynamic chains. We describe an effective algorithm for successively computing an infinite set of three-dimensional conservation laws for the Benney pair of commuting flows.
Keywords: integrable system, overdetermined system, hydrodynamic Benney chain, Kadomtsev–Petviashvili equation, three-dimensional conservation law. 
@article{TMF_2018_194_2_a6,
     author = {Z. V. Makridin},
     title = {An~effective algorithm for finding multidimensional conservation laws for integrable systems of hydrodynamic type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {320--330},
     publisher = {mathdoc},
     volume = {194},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a6/}
}
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Z. V. Makridin. An~effective algorithm for finding multidimensional conservation laws for integrable systems of hydrodynamic type. Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 2, pp. 320-330. http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a6/