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TMF, 2014, Volume 181, Number 1, Pages 155–172 (Mi tmf8724)  

Löwner evolution and finite-dimensional reductions of integrable systems

M. V. Pavlovab, D. V. Prokhorovc, A. Yu. Vasilievd, A. M. Zaharovc

a Lebedev Physical Institute, RAS, Moscow, Russia
b National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russia
c Saratov State University, Saratov, Russia
d Department of Mathematics, University of Bergen, Bergen, Norway

Abstract: 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, Vlasov equation, Benney moment, collisionless kinetic equation, Hamiltonian structure, hydrodynamic chain, hydrodynamic reduction

DOI: https://doi.org/10.4213/tmf8724

Full text: PDF file (467 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 181:1, 1263–1278

Bibliographic databases:

Received: 04.06.2014

Citation: M. V. Pavlov, D. V. Prokhorov, A. Yu. Vasiliev, A. M. Zaharov, “Löwner evolution and finite-dimensional reductions of integrable systems”, TMF, 181:1 (2014), 155–172; Theoret. and Math. Phys., 181:1 (2014), 1263–1278

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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