Constrained reductions of two-dimensional dispersionless Toda hierarchy, Hamiltonian structure, and interface dynamics

Journal of Mathematical Physics

Volumn 46, Issue 11, 2005, Pages

  Harnad, J ^a   Loutsenko, I ^b   Yermolayeva, O ^c  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c SISSA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 28844468865     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2104307     Document Type: Article

References (21)

1. Agam, O., Bettelheim, E., Wiegmann, P., and Zabrodin, A., " Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime., " Phys. Rev. Lett. 88, 236801 (2002), cond-mat/0111333.
2. Carlet G., " Extended Toda hierarchy and its Hamiltonian structure., " Ph.D. thesis, SISSA preprint 2003/FM.
3. Dickey, L. A., Soliton Equations and Hamiltonian systems, 2nd ed., Advanced Series in Mathematical Physics, Vol. 26 (World Scientific, River Edge, NJ, 2003).
4. "Dynamics of curved fronts", edited by, P. Pelc, in Perspectives in Physics (Academic, Boston, MA, 1988), Vol. xvi, 514 pp.
5. Enriques, B., Orlov, A., and Rubtsov, V., " Dispersionful analogues of Benney's equations and N-wave systems., " Inverse Probl. 12, 241-250 (1996).
6. Galin, L. A., " Unsteady filtration with a free surface., " C. R. (Dokl.) Acad. Sci. URSS 47, 246-249 (1945).
7. Howison, S. D., " Fingering in Hele-Shaw cells., " J. Fluid Mech. 167, 439-453 (1986).
8. Krichever, I., " The τ -function of the universal Whitham hierarchy, matrix models and topological field theories., " Commun. Pure Appl. Math. 47, 437-475 (1994).
9. Mineev-Weinstein, M., " Selection of the Saffman-Taylor finger width in the absence of surface tension: An exact result., " Phys. Rev. Lett. 80, 2113-2116 (1998).
10. Mineev-Weinstein M., and Dawson, S. P., " A new class of nonsingular exact solutions for Laplacian pattern formation., " Phys. Rev. E 1063-651X 10.1103/PhysRevE.50.R24 50, R24-R27 (1994), patt-sol/9305010; Mineev-Weinstein M. and Dawson, S. P. Phys. Rev. E 57, 3063-3072 (1998).
11. Mineev-Weinstein M., and Dawson, S. P., " A new class of nonsingular exact solutions for Laplacian pattern formation., " Phys. Rev. E 1063-651X 10.1103/PhysRevE.50.R24 50, R24-R27 (1994), patt-sol/9305010; Mineev-Weinstein M. and Dawson, S. P. Phys. Rev. E 57, 3063-3072 (1998).
12. Mineev-Weinstein, M., Wiegmann, P., and Zabrodin, A., " Integrable structure of interface dynamics., " Phys. Rev. Lett. 84, 5106-5109 (2000).
13. Orlov, A. Yu., and Schulman, E. I., " Additional symmetries for integrable equations and conformal algebra representation., " Lett. Math. Phys. 12, 171-179 (1986).
14. Pavlov, M. V., " Exact integrability of a system of Benney equations., " Dokl. Akad. Nauk 0869-5652 339, 311-313 (1994); Pavlov, M. V. translation in Phys. Dokl. 39, 745-747 (1994).
15. Pavlov, M. V., " Exact integrability of a system of Benney equations., " Dokl. Akad. Nauk 0869-5652 339, 311-313 (1994); Pavlov, M. V. translation in Phys. Dokl. 39, 745-747 (1994).
16. Polubarinova-Kotschina, P. J., " On the displacement of the oil-bearing contour., " C. R. (Dokl.) Acad. Sci. URSS 47, 250-254 (1945).
17. Richardson S., " Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel., " J. Fluid Mech. 56, 609-618 (1972).
18. Saffman, P. G., and Taylor, G., " The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid., " Proc. R. Soc. London, Ser. A 245, 312-329 (1958). (2 plates).
19. Takasaki, K., and Takebe, T., " Integrable hierarchies and dispersionless limit., " Rev. Math. Phys. 7, 743-808 (1995).
20. Takebe, T., " Toda lattice hierarchy and conservation laws., " Commun. Math. Phys. 129, 281-318 (1990).
21. Wiegmann, P. B., and Zabrodin, A., " Conformal maps and integrable hierarchies., " Commun. Math. Phys. 213, 523-538 (2000).