Two-dimensional discrete hydrodynamics and Monge-Ampère equations

Ergodic Theory and Dynamical Systems

Volumn 22, Issue 5, 2002, Pages 1575-1583

  Moser, Jürgen ^a   Veselov, Alexander P ^b,c  

^a ETH ZURICH   (Switzerland)

^b LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^c LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036801917     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385702001049     Document Type: Article

References (17)

1. V.I. Arnold. Mathematical Methods of Classical Mechanics. Springer, 1978.
2. R. Courant and D. Hilbert. Methods of Mathematical Physics II. Interscience, New York, 1962.
3. P. Hartman and L. Nirenberg. On spherical image maps whose Jacobians do not change sign. Amer. J. Math. 81 (1959), 901-920.
4. 2 = 1. Math. Ann. 127 (1954), 130-134.
5. J. Moser and A.P. Veselov. Discrete version of some classical integrable systems and factorization of matrix polynomials. Commun. Math. Phys. 139 (1991), 217-243.
6. J. Moser and A.P. Veselov. Two dimensional 'discrete hydrodynamics' and Monge-Ampère equation. Preprint, FIM, ETH, Zurich, 1993.
7. A.P. Veselov. Integrable Lagrangian correspondences and factorization of matrix polynomials. Funct. Anal. Appl. 25(2) (1991), 38-49.
8. A.P. Veselov. Integrable systems with discrete time and difference operators. Funct. Anal. Appl. 22(2) (1988), 1-13.
9. E. Goursat. Lecons sur l'intégration des équations aux dérivées partielles du second ordre á deux variables indépendantes, t. 1. Hermann, Paris, 1896.
10. 2 = 0. Pacific J. Math. 3 (1953), 165-187.
11. L.V. Ovsyannikov. Lectures on the Fundamentals of Gas Dynamics. Nauka, Moscow, 1981 (in Russian).
12. L.V. Ovsyannikov. Isobaric gas flows. Diff. Eqns 30(10) (1994), 1656-1662.
13. A.S. Zilbergleit. Exact solution of a nonlinear system of partial differential equations arising in hydrodynamics. Phys. Dokl. 38(2) (1993), 61-63.
14. D. Ban and T. Ratiu. On the geometrical origin and the solutions of a degenerate Monge-Ampère equation. Differential Geometry (Proc. Symp. Pure Math., 54(1)). American Mathematical Society, Providence, RI, 1993, pp. 55-68.
15. P.A. Shirokov and A.P. Shirokov. Affine Differential Geometry. GIFML, Moscow, 1959 (in Russian).
16. A.V. Penskoi. Discrete Lagrangian systems on the Virasoro group. Vestnik Moskov. Univ. Ser. 1, 1996, no. 4, 99-102.
17. A.V. Penskoi. Lagrangian time-discretization of the Korteweg-de Vries equation. Phys. Lett. A 269(4) (2000), 224-229.