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Two-dimensional ‘discrete hydrodynamics’ and Monge–Ampere equations
journal contribution
posted on 2006-06-23, 14:30 authored by J. Moser, Alexander VeselovAlexander VeselovAn integrable discrete-time Lagrangian system on the group of area-preserving
plane diffeomorphisms SDiff (R2) is considered. It is shown that non-trivial dynamics
exists only for special initial data and the corresponding mapping can be interpreted as
a Backlund transformation for the (simple) Monge–Ampere equation. In the continuous
limit, this gives the isobaric (constant pressure) solutions of the Euler equations for an ideal
fluid in two dimensions. In the Appendix written by E. V. Ferapontov and A. P. Veselov, it
is shown how the discrete system can be linearized using the transformation of the simple
Monge–Ampere equation going back to Goursat.
History
School
- Science
Department
- Mathematical Sciences
Pages
103555 bytesCitation
MOSER and VESELOV, 2002. Two-dimensional ‘discrete hydrodynamics’ and Monge–Ampere equations. Ergodic theory and dynamical systems, 22, pp. 1575–1583Publisher
© Cambridge University PressPublication date
2002Notes
This article was published in the journal, Ergodic theory and dynamical systems [© Cambridge University Press] and is available at: http://journals.cambridge.org/action/displayJournal?jid=ETS .ISSN
0143-3857Language
- en