Hirota quadratic equations for the extended Toda hierarchy
نویسندگان
چکیده
منابع مشابه
Tau Function and Hirota Bilinear Equations for the Extended Bigraded Toda Hierarchy
The Toda lattice equation is a nonlinear evolutionary differential-difference equation introduced by Toda [1] describing an infinite system of masses on a line that interact through an exponential force which is used to explain the well-known FermiPasta-Ulam phenomenon. It was soon realized that this equation is completely integrable, i.e. admits infinite conserved quantities. It has important ...
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The quasiclassical solution to the extended Toda chain hierarchy, corresponding to the deformation of the simplest Seiberg-Witten theory by all descendants of the dual topological string model, is constructed explicitly in terms of the complex curve and generating differential. The first derivatives of prepotential or quasiclassical tau-function over the extra times, extending the Toda chain, a...
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String equations of the p-th generalized Kontsevich model and the compactified c = 1 string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to a hypothesis postulated in the literature, the generalized Kontsevich model at p = −1 does not coincide with the c = 1 string theory at self-dual radius. A broader family of solutions of the Toda lattice hierarchy includi...
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The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy). Dispersionless limit of this multi-component hierarchy is considered on the level of the τ -function. The so called dispersionless Hirota equations are obtained from the Hirota equations of the τ -function. These dispersionless Hirota equations turn out to be equivalent to a system of Hamilton-Jacobi equations. Other relevant...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2007
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-07-13815-8