It is well known that the classical string on a two-sphere is more or less equivalent to the sine-Gordon model. We consider a system which can be understood as a T-dual to the classical string on a two-sphere. We show that there is a projection map from the phase space of this model to the phase space of the sine-Gordon model. The corresponding Poisson structure of the sine-Gordon model is nonl...

The internal motions of biomatter immersed in biofluid are investigated. The interactions between the fragments of biomatter and its surrounding biofluid are modeled using field theory. In the model, the biomatter is coupled to the gauge field representing the biofluid. It is shown that at non-relativistic limit various equation of motions, from the well-known Sine-Gordon equation to the simult...

The sine-Gordon equation with periodic boundary conditions describes integrable dynamics on the space of closed curves of constant torsion, for which multi-phase solutions provide large classes of canonical knot representatives. In this letter we discuss the use of Bäcklund transformations for studying the topological properties and symmetries of multi-phase solutions and of their homoclinic ma...

Two families of solutions of a generalized non-Abelian Toda lattice are considered. These solutions are expressed in terms of quasideterminants, constructed by means of Darboux and binary Darboux transformations. As an example of the application of these solutions, we consider the 2-periodic reduction to a matrix sine-Gordon equation. In particular, we investigate the interaction properties of ...

The focal point of this paper is a nonlinear model which describes localized magnetohydrodynamic modes in reversed-field pinch experiments. To date, nearly all experimental and theoretical work in this area have relied on the use of Fourier decomposition of spatial variations as a function of time. Moreover, due to the complexity of this nonlinear problem, previous work is restricted to the ana...

We establish the existence of homoclinic orbits for the near{integrable double discrete sine-Gordon (dDSG) equation under periodic boundary conditions. The hyperbolic structure and homoclinic orbits are constructed through the B acklund transformation and Lax pair. A geometric perturbation method based on Mel'nikov analysis is used to establish necessary criteria for the persistent of temporal...

We give arguments for the existence of exact travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. Such solutions are allowed exactly by the energy balance of these terms, and can be observed experimentally e....

We extend the action for evolution equations of KdV and MKdV type which was derived in NC] to the case of not periodic, but only equivariant phase space variables, introduced in FV2]. The diierence of these variables may be interpreted as reduced phase space variables via a Marsden-Weinstein reduction where the monodromies play the role of the momentum map. As an example we obtain the doubly di...

The BB acklund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constant torsion. We study its eeects on closed curves (in particular, elastic rods) that generate multiphase solutions for the vortex lament ow (also known as the Localized Induction Equation). In doing so...

We propose a spin-like model of DNA nonlinear dynamics with long-range interactions between adjacent base pairs. We show that the model equation is a modified sine-Gordon equation. We perform the linear stability analysis of a plane wave, which predicts high amplitude and extended oscillating waves for high values of the long-range parameter. This is confirmed numerically and biological implica...