Loewner evolution and finite dimensional reductions of integrable systems

Abstract

The Loewner equation is known as a one-dimensional reduction of the Benney chain as well as the dispersionless KP hierarchy. We propose a reverse process showing that time splitting in the Loewner or the Loewner-Kufarev equation leads to some known integrable systems.

References in corpus (2)

• Algebro-geometric approach in the theory of integrable hydrodynamic type systems
• Löwner equations and dispersionless hierarchies