Abstract The partition function of the Symmetric Matrix Ensemble is identified with $$\tau $$ ? -function a particular solution Pfaff Lattice. We show that, in case even power interactions, thermodynamic limit, corresponds to an integrable chain hydrodynamic type. prove that so obtained diagonalisable and adm...

In integrable field theories the S-matrix is usually a product of a relatively simple matrix and a complicated scalar factor. We make an observation that in many relativistic integrable field theories the scalar factor can be expressed as a convolution of simple kernels appearing in the nested levels of the nested Bethe ansatz. We formulate a proposal, up to some discrete ambiguities, how to re...

We show that for a one-dimensional Schrödinger operator with a potential, whose (j + 1)-th moment is integrable, the j-th derivative of the scattering matrix is in the Wiener algebra of functions with integrable Fourier transforms. We use this result to improve the known dispersive estimates with integrable time decay for the one-dimensional Schrödinger equation in the resonant case.

such that i) the geodesic flow on MA is (Liouville) integrable by C ∞ first integrals; ii) the geodesic flow on MA is not (Liouville) integrable by real-analytic first integrals; iii) the topological entropy of the geodesic flow Ft is positive; iv) the fundamental group π1(MA) of the manifold MA has an exponential growth; v) the unit covector bundle SMA contains a submanifold N such that N is d...

We present an algorithm for finding closed form solutions in elliptic functions of completely integrable systems. First we solve the linear differential equations in spectral parameter of Hermite-Halphen type. The integrability condition of the pair of equations of HermiteHalphen type gives the large family of completely integrable systems of Lax-Novikov type. This algorithm is implemented on t...

The relation between the dilatation operator of N = 4 Yang-Mills theory and integrable spin chains makes it possible to compute the one-loop anomalous dimensions of all operators in the theory. In this paper we show how to apply the technology of integrable spin chains to the calculation of Yang-Mills correlation functions by expressing them in terms of matrix elements of spin operators on the ...

Efficiency of time-evolution of quantum observables, and thermal states of quenched hamiltonians, is studied using time-dependent density matrix renormalization group method in a family of generic quantum spin chains which undergo a transition from integrable to non-integrable quantum chaotic case as control parameters are varied. Quantum states (observables) are represented in terms of matrix-...

We consistently develop a recently proposed scheme of matrix extension dispersionless integrable systems for the general case multidimensional hierarchies, concentrating on dimension $d\geqslant 4$. present extended Lax pairs, Lax-Sato equations, equations background vector fields and dressing scheme. Reductions, construction solutions connections to geometry are discussed. consider separately ...

Two standard tools for signal analysis are the short{time Fourier transform and the continuous wavelet transform. These tools arise as matrix coeecients of square integrable representations of the Heisenberg and aane groups respectively, and discrete frame decompositions of L 2 arise from approximations of corresponding reproducing formulae. Here we study two groups, the so-called aane Weyl-Hei...