Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

A geometric approach to immersion formulas for soliton surfaces is provided via a generalization of the de Rham cohomology and its differential to a space of Lie algebra-valued differential forms parametrised by a spectral parameter. This leads to introducing new Poincare type lemmas for such cohomologies, which appropriately describe integrability conditions and deformations of Lax pairs. In this language, properties of soliton surfaces, e.g. immersion formulas, become very simple and generalizations of 2D-models to soliton submanifolds appear straightforwardly. Theoretical results are illustrated by physical examples.