The generating functional of correlation functions for theXXZ spin chain is considered in the thermodynamic limit. We derive a system of integro-difference equations that prescribe this functional. On the basis of this system we establish the operator-valued Riemann–Hilbert problem for correlation functions of the XXZ spin chain.

In this paper I continue the study of the new nonperturbative framework of modular localization and its constructive use in the d=1+1 KarowskiWeisz-Smirnov formfactor program. Particular attention is focussed on the connection of the (Zamolodchikov) algebraic structure and its relation to the Riemann-Hilbert problem for wedge localized multiparicle wave functions in the incoming Fock space and ...

An efficient formalism is elaborated to analytically describe dynamics of the Ablowitz-Ladik soliton in the presence of perturbations. This formalism is based on using the Riemann-Hilbert problem and provides the means of calculating evolution of the discrete soliton parameters, as well as shape distortion and perturbation-induced radiation effects. As an example, soliton characteristics are ca...

We present a 3×3 Riemann-Hilbert problem formalism for the initial-boundary value of two-component nonlinear Schrödinger (2-NLS) equation on half-line. And we also get Dirichlet to Neuemann map through analysising global relation in this paper.

\Ve consider the direct and inverse scattering for the n-dimensional Schrodinger equation, n 2: 2, with a potential having no spherical symmetry. Sufficient conditions are given for the existence of a Wiener-Hopf factorization of the corresponding scattering operator. This factorization leads to the solution of a related Riemann-Hilbert problem, which plays a key role in inverse scattering.

We consider a wireless communication device that uses network coding and acts as a relay for two connections. We analyze a two-dimensional continuous-time queueing model of the system and show that steady-state performance can be expressed in the solution of a Riemann-Hilbert boundary value problem. From this solution we derive the expected energy consumption and expected packet delay.

By using Riemann–Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants detN [ cla−mb [ f ] ] generated by holomorhpic symbols, where la = a (resp. mb = b) except for a finite subset of indices a = h1, . . . , hn (resp. b = t1, . . . , tr). In addition to the usual Szegö asymptotics, our answer involves a determinant of size n + r.

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...

We correct a wrong argument in Proposition 3.3. show how to get around this error. For that purpose, Sections 3.2– 3.4 of the main text have be replaced with E.3.2–E.3.4-E.3.2–E.3.4 below (Sections 3.1 and 3.5 remain unchanged). The change is new statement E.3.3 (which essentially corresponds Corollary published text) its proof. end proof Theorem 3 has been adapted correspondingly. As consequen...

Last three years have seen new developments in the theory of last passage percolation, which has variety applications to random permutations, random growth and random vicious walks. It turns out that a few class of models have determinant formulas for the probability distribution, which can be analyzed asymptotically. One of the tools for the asymptotic analysis has been the Riemann-Hilbert met...