Related papers: Tau-function for discrete sine-Gordon equation and…
In this paper, we propose fully discrete analogues of a generalized sine-Gordon (gsG) equation $u_{t x}=\left(1+\nu \partial_x^2\right) \sin u$. The bilinear equations of the discrete KP hierarchy and the proper definition of discrete…
We define two tau functions, $\tau$ and $\hat{\tau}$ , on moduli spaces of spectral covers of $GL(n)$ Hitchin's systems. Analyzing the properties of $\tau$, we express the divisor class of the universal Hitchin's discriminant in terms of…
We analyze isomonodromic deformations of rational connections on the Riemann sphere with Fuchsian and irregular singularities. The Fuchsian singularities are allowed to be of arbitrary resonant index; the irregular singularities are also…
Sato theory provides a correspondence between solutions to the KP hierarchy and points in an infinite dimensional Grassmannian. In this correspondence, flows generated infinitesimally by powers of the ``shift'' operator give time dependence…
We derive non-linear differential equations for correlation functions of U(1) twist fields in the two-dimensional massive Dirac theory. Primary U(1) twist fields correspond to exponential fields in the sine-Gordon model at the free-fermion…
We provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood--Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur…
In this work we deform the phi^4 model with distinct deformation functions, to propose a diversity of sine-Gordon-like models. We investigate the proposed models and we obtain all the topological solutions they engender. In particular, we…
In this paper, the relationship between the sine-Gordon model with an integrable boundary condition and the Thirring model with boundary is discussed and the reflection $R$-matrix for the massive Thirring model, which is related to the…
We present an analytic study of the finite size effects in Sine--Gordon model, based on the semiclassical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi--periodic kink is realized as an elliptic…
In this paper, we formulate and present ample evidence towards the conjecture that the partition function (i.e. the exponential of the generating series of intersection numbers with monomials in psi classes) of the Pixton class on the…
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a…
Initial-boundary value problems for complex sine-Gordon and sine-Gordon equations in a semi--strip are treated. The evolution of the Weyl function and a uniqueness result are obtained for complex sine-Gordon equation. The evolution of the…
The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the $A_{3}$-generalization where fields take value in $SU(2)$ describes integrable deformations of conformal field…
The most basic characteristic of x-quasiperiodic solutions u(x,t) of the sine-Gordon equation u_{tt}-u_{xx}+\sin u=0 is the topological charge density denoted $\bar n$. The real finite-gap solutions u(x,t) are expressed in terms of the…
The solitons and kinks of the generalized $sl(3, \IC)$ sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the {\sl tau} functions play an important role. The various properties are…
We consider the probability to find a string of $x$ adjacent parallel spins in the antiferromagnetic ground state of the model (in a magnetic field). We derive a system of integro-difference equations which define this probability. This…
This is the third in a series of papers attempting to describe a uniform geometric framework in which many integrable systems can be placed. A soliton hierarchy can be constructed from a splitting of an infinite dimensional group $L$ as…
The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows for its eigenstates to be constructed algebraically. In this work we show that quantum…
In this paper we study Baker-Akhiezer spinor kernel on moduli spaces of meromorphic differentials on Riemann surfaces. We introduce the Baker-Akhiezer tau-function which is related to both Bergman tau-function (which was studied before in…
This contribution to the Proceedings of the Workshop on Integrable Theories, Solitons and Duality in Sao Paulo in July 2002 summarizes results from the papers hep-th/0112023 and math.QA/0208043. We derive the non-local conserved charges in…