Negatons of the Korteweg-de Vries equation

In the talk we explain an operator-theoretic approach to the Korteweg-de Vries equation. Using the theory of determinants on quasi-Banach ideals as fundamental tool, we derive a solution formula, which contains an operator-valued parameter.

It can be shown that all solutions covered by the Inverse Scattering Method (and more) can be realized in this frame.

As an application we discuss negatons, a solution class with the following properties: They consist of solitons which are organized in groups, and solitons in the same group are weakly coupled. In contrast groups as a whole show a particle-like behaviour. Within our formalism negatons corrsepond to the case of finite-dimensional parameters.

Our main result is the complete characterization of negatons in terms of their long-time behaviour.