Titlebook: Integrable Hierarchies and Modern Physical Theories; Henrik Aratyn,Alexander S. Sorin Book 2001 Springer Science+Business Media Dordrecht

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Integrable Hierarchies in Donaldson-Witten and Seiberg-Witten Theories,in Donaldson-Witten theory, up to a redefinition of the fast times, is a τ-function for a .-gap solution of the KdV hierarchy. In the case of four-manifolds of simple type, instead, the blowup function becomes a τ-function corresponding to a multisoliton solution. We obtain a new expression for the

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amphibian

Reflection Amplitudes in Conformal Field Theory and Integrable Systems,acuum expectation values of exponential fields in affine Toda theories and related perturbed conformal field theories. We calculate also the asymptotics of cylindrically symmetric solutions of the classical Toda equations. The integrable boundary Toda theories are considered. We derive boundary refl

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New Solvable Periodic Potentials from Supersymmetry,in the energy band structure of the Lamé potentials .sn.(.) and associated Lamé potentials .sn.(., .) + .cn.(.)/dn. (.), both of which involve Jacobi elliptic functions with modulus parameter .. We find several new analytic expressions for band edge energies and wave functions. The supersymmetric pa

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Integrable Multidimensional Discrete Geometry,enting geometric interpretation of various soliton fields (for example, the τ function) used to describe the quadrilateral lattices we discuss the Darboux-type transformations of the lattices. Then we list the basic reductions of the quadrilateral lattice and we present their geometric properties. F

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Integrable Nets and the KP Hierarchy,study of conjugate, orthogonal and Egorov nets. We also discuss the appearance of integrable lattices in this context. Finally, we also treat the τ-formulation, vertex operators and Miwa transformations for these geometric nets.

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