A soliton is a wave packet that travels through a dispersive and nonlinear medium at the same time and still propagates without changing its shape. Even if two solitons collide, they continue to run unharmed afterwards.
A wave packet consists of several frequencies. If the speed of propagation in the medium is different at different frequencies (known as dispersion), the packet will become deformed and wider over time. Non-linear effects convert the individual frequencies that make up a wave packet into one another. If this happens in such a way that the faster frequency components are converted into slower ones and slower ones into faster ones, a dynamic equilibrium can develop in which the shape of the wave remains unchanged: a soliton.
The phenomenon of solitons was first described in 1834 by the young engineer John Scott Russell. Russell rode several kilometers alongside a wave of water about 10 meters long and half a meter high, which was spreading in a narrow Scottish channel, and observed that the wave shape changed very little.

## Model of topological solitons

An approach to the description of elementary particles and their interactions, which is fundamentally different from quantum field theory, is based on the description using topologically stable field distributions. This 3+1-dimensional model is based on a 1+1-dimensional (mechanical) model that can be brought closer to understanding and imagination by means of a pendulum chain.

These solitons have properties that suggest they should be associated with those of a relativistic particle. This website is intended to give a brief overview of the properties involved and how they come about.

## Mechanical, one-dimensional soliton model

This simple model, which can be used to illustrate the most important properties of solitons in 1+1 dimensions (1 spatial coordinate or the time t), is a discrete pendulum chain (Fig. 1).

These are pendulums arranged in a line and connected to each other by springs. The following forces are at work in such a pendulum chain:

• torsional forces

• gravity