Related papers: The Kirchhoff Rod as a XY Spin Chain Model
We consider here the massive Thirring model regularized with the XYZ spin chain. We numerically calculate the mass ratios of particles which lie in the discrete part of the spectrum and obtain results in accordance with the DHN formula and…
The Klein-Fock-Gordon equation is studied on the generalized Y-junction of $N$ strings with a massive center. The corresponding formulas for wave scattering and normal modes are obtained.
A new approach for investigating the classical dynamics of the relativistic string model with rigidity is proposed. It is based on the embedding of the string world surface into the space of a constant curvature. It is shown that the rigid…
We report a two-dimensional (2D) gravitating kink model, for which both the background field equations and the linear perturbation equation are exactly solvable. The background solution describes a sine-Gordon kink that interpolating…
We investigate a family of curve evolution equations approximating the motion of a Kirchhoff rod immersed in a low Reynolds number fluid. The rod is modeled as a framed curve whose energy consists of the bending energy of the curve and the…
We study travelling kinks in the spatial discretizations of the nonlinear Klein--Gordon equation, which include the discrete $\phi^4$ lattice and the discrete sine--Gordon lattice. The differential advance-delay equation for travelling…
A s=1/2 antiferromagnetic spin chain is equivalent to the two-flavor massless Schwinger model in an uniform background charge density in the strong coupling. The gapless mode of the spin chain is represented by a massless boson of the…
In this paper we consider a Robin problem for the Klein-Gordon equation in a doubly connected domain. The solution domain considered is a bounded smooth doubly connected planar domain bounded by two simple disjoint closed curves. The…
We analyse several physical aspects of the dressed elliptic strings propagating on $\mathbb{R} \times \mathrm{S}^2$ and of their counterparts in the Pohlmeyer reduced theory, i.e. the sine-Gordon equation. The solutions are divided into two…
Beck's type column on Winkler type foundation is the subject of the present analysis. Instead of the Bernoulli-Euler model describing the rod, two generalized models will be adopted: Eringen non-local model corresponding to nano-rods and…
We study the XXZ Heisenberg model in a longitudinal magnetic field using a tensor renormalization method. Built into the tensor representation of the XXZ model is the U(1) symmetry, which is systematically maintained at each renormalization…
We study small perturbations around an arbitrary static kink solution of a two-dimensional (2D) gravity-scalar system, where the gravity part is described by a subclass of 2D dilaton gravity theory, and the scalar matter field has…
Brane model of universe is considered for a free particle. Conservation laws on the brane are obtained using the symmetry properties of the brane. Equation of motion is derived for a particle using variation principle from these…
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…
We consider linearly stable elliptic fixed points for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. Morbidelli and Giorgilli have proved a theorem of stability over…
We prove the existence of at least two geometrically different periodic solution with winding number N for the forced relativistic pendulum. The instability of a solution is also proved. The proof is topological and based on the version of…
This paper presents a comprehensive analysis of several aspects of the sinh-Gordon equation within a periodic setting. Our investigation proceeds in three main stages. First we establish the existence of periodic solutions for a fixed wave…
In this article, we study a double-phase variable-exponent Kirchhoff problem and show the existence of at least three solutions. The proposed model, as a generalization of the Kirchhoff equation, is interesting since it is driven by a…
Using a collective-mode Monte Carlo method (the Wolff-Swendsen-Wang algorithm), we compute the spin-stiffness of the two-dimensional classical Heisenberg model. We show that it is the relevant physical quantity to investigate the behaviour…
Highly spinning classical strings on RxS^3 are described by the Landau-Lifshitz model or equivalently by the Heisenberg ferromagnet in the thermodynamic limit. The spectrum of this model can be given in terms of spectral curves. However, it…