The Eccentrics Under the Waves
Solitons are waves that travel long distances with seemingly no loss of energy. Although we encounter them all the time in everyday life, most scientists ignore them. With a new theory that works with operators, all classes of solitons can now be described relatively easily. Solitons are not a new currency, not a mysterious bacterium, but the name of a mathematical and scientific phenomenon. In terms of topicality, soliton research is in no way inferior to the spectacular economic or microbiological investigations. After all, the soliton is an everyday occurrence. At the Friedrich Schiller University in Jena, the mathematicians led by Prof. Dr. Bernd Carl and Dr. Cornelia Schiebold found an unconventional, relatively simple solution to tackle the problem.
Solitons are single, very stable forms of waves that do not change in speed, size and appearance - a phenomenon that amazes all of us. One can observe solitons on any holiday at the sea. Solitons occur in every hurricane, in sunlight or in the swell on the beach, is how Bernd Carl describes the everyday significance of his theoretical research. But solitons also play a key role in plasma physics, gravitational theory and climate research, as an explanation model for the pulse, to describe ecological systems, in nonlinear optics or in thermodynamics. After all, it's about grasping the non-linear, complex interrelationships of the world, and ultimately we haven't understood this non-linear world adds Cornelia Schiebold.
Solitons were discovered in 1834 by John Scott Russell. The Scot rode for miles next to a singular wave crest (Fig. 102K) - which had probably been triggered by a ship's bow in an inland canal - without the shape and speed of the wave having changed. Since then, scientists and mathematicians have been gripped by the soliton puzzle. Korteweg and de Vries first described it abstractly but incompletely with differential equations in 1895.
Today, the mathematicians in Jena can offer a theory with the help of geometric and functional analysis, which should ensure uniform access to all existing solution classes, i.e. it covers all known types of solitons. What is new about it is that – instead of the previous approaches using the formation of a soliton – a comparatively easy-to-handle operator-theoretical model is used. With this, even new classes of solitons can be constructed and described geometrically.
These operator methods will definitely play a role in scientific calculations explains Cornelia Schiebold. However, when it comes to solitons, the Jena-based company is way ahead of the game with their theory; concrete applications for the new solutions are still waiting to be discovered. But the mathematicians do not see themselves as assistant scientists to their colleagues in physics, chemistry and biology. In abstract dimensions we think much further than the concrete world reveals, Bernd Carl describes his field as an intellectual adventure.
The Heidelberger Verlag Spektrum der Wissenschaft is the operator of this portal. Its online and print magazines, including "Spektrum der Wissenschaft", "Gehirn&Geist" and "Spektrum – Die Woche", report on current research findings.