Witten solution of the Gelfand - Dikii hierarchy
نویسنده
چکیده
We produce formulas, permiting to find the coefficients of Taylor–series expanded of some important solution of the Gelfand-Dikii hierarchy. By the Witten conjecture these coefficients are numbers of intersection of Mumford-Morita-Muller stable cohomological classes of moduli space of n-spin bundles on Riemann surfaces with punctures .
منابع مشابه
Singular sector of the KP hierarchy, ∂̄-operators of non-zero index and associated integrable systems
Integrable hierarchies associated with the singular sector of the KP hierarchy, or equivalently, with ∂̄-operators of non-zero index are studied. They arise as the restriction of the standard KP hierarchy to submanifols of finite codimension in the space of independent variables. For higher ∂̄-index these hierarchies represent themselves families of multidimensional equations with multidimensiona...
متن کاملeb 2 00 3 Additional symmetries and solutions of the dispersionless KP hierarchy ∗ Luis
The dispersionless KP hierarchy is considered from the point of view of the twistor formalism. A set of explicit additional symmetries is characterized and its action on the solutions of the twistor equations is studied. A method for dealing with the twistor equations by taking advantage of hodograph type equations is proposed. This method is applied for determining the orbits of solutions sati...
متن کاملAnalytical Solution of the Sl(2,r)/u(1) Wznw Black Hole Model
The gauged SL(2,R)/U(1) Wess-Zumino-Novikov-Witten (WZNW) model is classically an integrable conformal field theory. We have found a Lax pair representation for the non-linear equations of motion, and a Bäcklund transformation. A second-order differential equation of the Gelfand-Dikii type defines the Poisson bracket structure of the theory, and its fundamental solutions describe the general so...
متن کاملOn Commuting Differential Operators
The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations Ly = zy, z ∈ C, are meromorphic. In this paper this relationship is explored ...
متن کاملHamiltonian Formalism of Whitham-Type Hierarchies and Topological Landau-Ginsburg Models
We show that the bi-hamiltonian structure of the averaged Gelfand-Dikii hierarchy is involved in the Landau-Ginsburg topological models (for An-Series): the Casimirs for the first P.B. give the correct coupling parameters for the perturbed topological minimal model; the correspondence {coupling parameters} ~ {primary fields} is determined by the second P.B. The partition function (at the tree l...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000