Related papers: Boundary sine-Gordon model
The exact solution of the boundary sine-Gordon model is studied in the region where the scaling dimension of the boundary field $1 < \Delta < 1$. It is shown that at $\Delta > 2/3$ the infrared fixed point belongs to the universality class…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…
The Poincar\'e-covariant quantum-field-theoretic description of bound states by the homogeneous Bethe-Salpeter equation usually exhibits an intrinsic complexity that can be attenuated by allowing this formalism to undergo various…
We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by…
The sine-Gordon model with space- and time-dependent parameters is considered. A highly accurate effective model with two degrees of freedom is constructed, allowing the description of the kink movement in this model even for extremely long…
This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the…
The question of the integrability of real-coupling affine toda field theory on a half line is discussed. It is shown, by examining low-spin conserved charges, that the boundary conditions preserving integrability are strongly constrained.…
We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we…
We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a…
We consider a scalar Hamiltonian nonlinear wave equation formulated on networks; this is a non standard problem because these domains are not locally homeomorphic to any subset of the Euclidean space. More precisely, we assume each edge to…
The sine-Gordon equation on a metric graph with a structure represented by a $\mathcal{Y}$-junction, is considered. The model is endowed with boundary conditions at the graph-vertex of $\delta'$-interaction type, expressing continuity of…
In this paper, we numerically study the scattering of kinks in the noncanonical sine-Gordon model using Fourier spectral methods. The model depends on two free parameters, which control the localized inner structure in the energy density…
In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. We focus in this paper on…
We consider integrable models of the Haldane-Shastry type with open boundary conditions. We define monodromy matrices, obeying the reflection equation, which generate the symmetries of these models. Using a map to the Calogero-Sutherland…
We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions, and show that in the quantum theory a remnant survives of the bulk quantized affine algebra symmetry generated by…
Abstarct: Boundary effects caused by the boundary interactions in various integrable field theories on a half line are discussed at the classical as well as the quantum level. Only the so-called ``integrable" boundary interactions are…
This work studies the dynamics of solutions to the sine-Gordon equation posed on a tadpole graph $G$ and endowed with boundary conditions at the vertex of $\delta$-type. The latter generalize conditions of Neumann-Kirchhoff type. The…
A model of soliton-defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for…
We consider the two-dimensional quantum field theory of a scalar field self-interacting via two periodic terms of frequencies $\alpha$ and $\beta$. Looking at the theory as a perturbed Sine-Gordon model, we use Form Factor Perturbation…
Using the recently introduced boundary form factor bootstrap equations, we map the complete space of their solutions for the boundary version of the scaling Lee-Yang model and sinh-Gordon theory. We show that the complete space of…