Hamiltonian flows of curves in and vector soliton equations of mKdV and sine-Gordon type.
Hamiltonian structure and new exact soliton solutions of some Korteweg--de Vries equations.
Hidden symmetries of integrable systems in Yang-Mills theory and Kähler geometry
Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem
This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators...
Hypersurface geometry and Hamiltonian systems of hydrodynamic type.