2134/2215
J. Moser
J.
Moser
Alexander Veselov
Alexander
Veselov
Two-dimensional ‘discrete hydrodynamics’ and Monge–Ampere equations
Loughborough University
2006
untagged
Mathematical Sciences not elsewhere classified
Computation Theory and Mathematics
2006-06-23 14:30:50
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Two-dimensional_discrete_hydrodynamics_and_Monge_Ampere_equations/9385613
An 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.