Geodesic
L\"owner evolution and finite-dimensional reductions of integrable systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 1, pp. 155-172

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The Löwner equation is known as the one-dimensional reduction of the Benney chain and also as the dispersionless KP hierarchy. We propose a reverse process and show that time splitting in the Löwner or the Löwner–Kufarev equation leads to some known integrable systems.
Keywords: Löwner equation, integrable system, Benney moment, collisionless kinetic equation, Hamiltonian structure, hydrodynamic reduction.
Mots-clés : Vlasov equation, hydrodynamic chain 
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     author = {M. V. Pavlov and D. V. Prokhorov and A. Yu. Vasiliev and A. M. Zaharov},
     title = {L\"owner evolution and finite-dimensional reductions of integrable systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {155--172},
     publisher = {mathdoc},
     volume = {181},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_181_1_a7/}
}
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M. V. Pavlov; D. V. Prokhorov; A. Yu. Vasiliev; A. M. Zaharov. L\"owner evolution and finite-dimensional reductions of integrable systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 1, pp. 155-172. http://geodesic.mathdoc.fr/item/TMF_2014_181_1_a7/