The generalized open XXZ model at q root of unity is considered. We review how associated models, such as the q harmonic oscillator, and the lattice sine-Gordon and Liouville models are obtained. Explicit expressions of the local Hamiltonian of the spin 1 2 XXZ spin chain coupled to dynamical degrees of freedom at the one end of the chain are provided. Furthermore, the boundary non-local charge...

This paper studies a perturbative approach for the double sine–Gordon equation. Following this path, we are able to obtain system of differential equations that shows amplitude and phase modulation approximate solution. In case λ = 0, get well-known perturbation theory For special value −1/8, derive phase-locked solution with same frequency linear case. general, both coherent (solitary waves, l...

In this work, we successfully construct the new exact traveling wave solutions of the generalized Sinh–Gordon equation by new application of the homogeneous balance method. The idea introduced in this paper can be applied to other nonlinear evolution equations.

A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two P(φ)2 systems with polynomial self-interactions.

As I briefly review, the sine-Gordon model may be obtained by dimensional and algebraic reduction from 2+2 dimensional self-dual U(2) Yang-Mills through a 2+1 dimensional integrable U(2) sigma model. I argue that the noncommutative (Moyal) deformation of this procedure should relax the algebraic reduction from U(2) → U(1) to U(2) → U(1)×U(1). The result are novel noncommutative sine-Gordon equa...

New aspects of the complex sine-Gordon theory are addressed through the reformulation of the theory in terms of the gauged Wess-Zumino-Witten action. A dual transformation between the theory for the coupling constant β > 0 and the theory for β < 0 is given which agrees with the Krammers-Wannier duality in the context of perturbed conformal field theory. The Bäcklund transform and the nonlinear ...

We have numerically investigated the dynamics of a long linear Josephson tunnel junction with overlap geometry (Flux-Flow Oscillator, FFO). The study is performed in the frame of a modified sine-Gordon model, which includes surface losses, self-pumping effect, and in an empirical way the superconducting gap. The electromagnetic coupling to the environment is modeled by a simple resistor-capacit...