Introduction. Elastic Ribbon Model.

The basic properties of solitons, like propagation and interaction without change in their velocity and shape, make it possible to treat them as the robust localized objects. Solitons show their duality, having both the properties of particles and waves. A soliton has the wave nature and finite width but it behaves itself as a particle when interacting with other solitons. That is why the solitons are often spoken of as quasiparticles. It is known that for solitons in a completely integrable system there exist an infinitely large number of conservation laws. For example, not only the energy and momentum but also a characteristic, which can be called "charge", is conserved in the system. There exist several physical interpretations of the sine-Gordon equation, therefore this charge will be called here the topological charge, without specification for a particular model.

Let us twist one end of the elastic ribbon with respect to another through angle 2 . As a result of this operation a twist, which can propagate along the ribbon, will be formed Ref. [1]. The ribbon can be twisted either clockwise or counterclockwise. Therefore, the twist can be regarded as a charged particle and the sign of charge is defined by the direction of twisting.