User Portlet

My research interests lie in the area of integrable systems, and related topics from algebraic geometry and theory of Lie groups and algebras. Under integrable systems I mean completely integrable hierarchies of soliton-type equations. I worked with KdV, mKdV, sine-Gordon, NLS, Heisenberg magnetic chain, and their multicomponent generalizations.

Now I focus on algebraic integration of such hierarchies in terms of $\wp$-functions, which generalize the Weierstrass $\wp$-function. This type of integration is closely related to uniformization of plane algebraic curves. And this is the part of algebraic geometry which attracts my interest.

I have learned the recently developed theory of multi-variable sigma functions, which offers a beautiful mathematical construction for deriving these functions as analytical series. As by-products of the theory of multi-variable sigma functions we obtain relations between their second and higher logarithmic derivatives, known as $\wp$-functions, addition laws, etc.

In my research I use symbolic and numerical computations in Mathematica, which I would like to share.