An algorithm for intelligent backtracking

Sato, Taisuke

doi:10.1007/3-540-11980-9_17

Cited by 45 publications

(88 citation statements)

References 2 publications

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“…The KP/Toda systems have infinite amount of solutions parameterized by so called infinite-dimensional Grassmannian (roughly speaking a function of two variables -the initial conditions) [31,32]. The particular solutions can be distinguished by additional (sometimes linear) equations, say, on the τ -function.…”

Section: Integrable Systemsmentioning

confidence: 99%

“…defined on the two-punctured sphere. Matrix (34) is almost three-diagonal as it follows from (31), the only extra nonzero elements appear in the off-diagonal corners exactly due to periodic conditions (32) reducing therefore naively infinite-dimensional matrix (31) to a finite-dimensional one depending on the spectral parameter w.…”

Section: Toda Chain: the Periodic Problemmentioning

confidence: 99%

“…An alternative description of the same system arises when one (before imposing periodic conditions) solves explicitly the auxiliary linear problem (31) which is a second-order difference equation. To do it one just rewrites (31) as…”

Section: Toda Chain: the Periodic Problemmentioning

confidence: 99%

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On integrable systems and supersymmetric gauge theories

Marshakov

1997

Theor Math Phys

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The properties of the N = 2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed.The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential are presented, the invariant sense of these definitions is illustrated.Recently found exact nonperturbative solutions to N = 2 SUSY gauge theories are formulated using the methods of the theory of integrable systems and where possible the parallels between standard quantum field theory results and solutions to integrable systems are discussed.

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Section: Integrable Systemsmentioning

confidence: 99%

Section: Toda Chain: the Periodic Problemmentioning

confidence: 99%

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On integrable systems and supersymmetric gauge theories

Marshakov

1997

Theor Math Phys

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“…It is known that a general class of Hirota's equations are related with the geometry of Grassmannian manifolds and can be constructed out of a general Young tableau. 10,11 If, for example, the Young diagrams Y = [a s2 1 , (a 1 + a 2 ) s1 ] consist of two rectangular blocks (one with a 1 lines of length s 1 + s 2 and the second with a 2 lines of length s 1 ), then the higher Hirota equations hold…”

Section: Introductionmentioning

confidence: 99%

Bethe Ansatz and Classical Hirota Equation

Wiegmann

1997

Int. J. Mod. Phys. B

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We discuss an interrelation between quantum integrable models and classical soliton equations with discretized time. It appeared that spectral characteristics of quantum integrable systems may be obtained from entirely classical set up. Namely, the eigenvalues of the quantum transfer matrix and the scattering $S$-matrix itself are identified with a certain $\tau$-functions of the discrete Liouville equation. The Bethe ansatz equations are obtained as dynamics of zeros. For comparison we also present the Bethe ansatz equations for elliptic solutions of the classical discrete Sine-Gordon equation. The paper is based on the recent study of classical integrable structures in quantum integrable systems, hep-th/9604080.Comment: 15 pages, Latex, special World Scientific macros include

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“…the "times" t k and the "point of the Sato Universal Grassmannian" g [4]. In particular our τ p (t) = τ (KP ) (t|g p ), and the question is what is the way to characterize the point g p ∈ GR without explicit reference to the matrix integral (2).…”

Section: Introductionmentioning

confidence: 99%

New matrix model solutions to the Kac-Schwarz problem

Adler¹,

Морозов²,

Shiota³

et al. 1996

Nuclear Physics B - Proceedings Supplements

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We examine the Kac-Schwarz problem of specification of point in Grassmannian in the restricted case of gap-one first-order differential Kac-Schwarz operators. While the pair of constraints satisfying $[{\cal K}_1,W] = 1$ always leads to Kontsevich type models, in the case of $[{\cal K}_1,W] = W$ the corresponding KP $\tau$-functions are represented as more sophisticated matrix integrals.Comment: 19 pages, latex, no figures, contribution to the proceedings of the 29th International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, German

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An algorithm for intelligent backtracking

Cited by 45 publications

References 2 publications

On integrable systems and supersymmetric gauge theories

On integrable systems and supersymmetric gauge theories

Bethe Ansatz and Classical Hirota Equation

New matrix model solutions to the Kac-Schwarz problem

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