Abstract
The Tau-Function
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References
Hirota, R. (1980) Direct methods in soliton theory, in: Solitons, Springer-Verlag, New York.
Date, E., Kashiwara, M., Jimbo, M., and Miwa, T. (1983) Transformation groups for soliton equations, in: Nonlinear integrable systems—classical theory and quantum theory (Kyoto, 1981), World Scientific, Singapore, pp. 39–119.
Sato, M. and Sato, Y. (1983) Soliton equations as dynamical systems on infinitedimensional Grassmann manifold, in: Nonlinear partial differential equations in applied science (Tokyo, 1982), North-Holland Math. Stud.,Vol. 81, North-Holland, Amsterdam, pp. 259–271.
Sato, M. (1989) The KP hierarchy and infinite-dimensional Grassmann manifolds, in: Theta functions—Bowdoin 1987, Part 1 (Brunswick, ME, 1987), Proc. Sympos. Pure Math., Vol. 49, Amer. Math. Soc., Providence, RI, pp. 51–66.
Kawamoto, N., Namikawa, Y., Tsuchiya, A., and Yasuhiko Yamada, (1988) Geometric realization of conformal field theory on Riemann surfaces, Comm. Math. Phys. 116(2), pp. 247–308.
Hirota, R. (1981) Discrete analogue of a generalized Toda equation, J. Phys. Soc. Japan 50(11), pp. 3785–3791. MR 83e:58035.
Takasaki, K. and Takebe, T. (1995) Integrable hierarchies and dispersionless limit, Rev. Math. Phys. 7(5), pp. 743–808.
Krichever, I. M. (1992) The dispersionless Lax equations and topological minimal models, Comm. Math. Phys. 143(2), pp. 415–429.
Krichever, I. M. (1994) The τ -function of the universal Whitham hierarchy, matrix models and topological field theories, Comm. Pure Appl. Math. 47(4), 437–475.
Adler, M. and van Moerbeke, P. (1992) A matrix integral solution to two dimensional Wp-gravity, Comm. Math. Phys. 147(1), pp. 25–56.
Boyarsky, A., Marshakov, A., Ruchayskiy, O., Wiegmann, P., and Zabrodin, A. (2001) Associativity equations in dispersionless integrable hierarchies, Phys. Lett. B 515(3–4), pp. 483–492.
Kirillov, A. A. (1987) Kähler structure on the K-orbits of a group of diffeomorphisms of the circle, Funktsional. Anal. i Prilozhen. 21(2), pp. 42–45.
Wiegmann, P. B. and Zabrodin, A. (2000) Conformal maps and integrable hierarchies, Comm. Math. Phys. 213(3), pp. 523–538.
Bers, Lipman. (1981) Finite-dimensional Teichmüller spaces and generalizations, Bull. Amer. Math. Soc. (N.S.) 5(2), pp. 131–172.
Nag, S. and Verjovsky, A. (1990) Diff(S1) and the Teichmüller spaces, Comm. Math. Phys. 130(1), pp. 123–138.
Krichever, I. M. (2000) unpublished manuscript.
Takhtajan, L. A. (2001) Free bosons and tau-functions for compact Riemann surfaces and closed smooth Jordan curves. Current correlation functions, Lett. Math. Phys. 56(3), pp. 181–228, EuroConférence Moshé Flato 2000, Part III (Dijon).
Kostov, I. K., Krichever, I., Mineev-Weinstein, M., Wiegmann, P. B., and Zabrodin, A. (2001) The τ -function for analytic curves, in: Random Matrix Models and their Applications, Math. Sci. Res. Inst. Publ., Vol. 40, Cambridge University Press, Cambridge, pp. 285–299.
Zabrodin, A. V. (2001) The dispersionless limit of the Hirota equations in some problems of complex analysis, Teoret. Mat. Fiz. 129(2), pp. 239–257.
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Takhtajan, L.A. (2006). FREE BOSONS AND DISPERSIONLESS LIMIT OF HIROTA TAU-FUNCTION. In: Faddeev, L., Van Moerbeke, P., Lambert, F. (eds) Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete. NATO Science Series, vol 201. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3503-6_26
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DOI: https://doi.org/10.1007/978-1-4020-3503-6_26
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