Soliton surfaces associated with sigma models: differential and algebraic aspects

Conformally parametrized surfaces associated with CPN−1 sigma models

Two-dimensional parametrized surfaces immersed in the su(N) algebra are investigated. The focus is on surfaces parametrized by solutions of the equations for the CP N−1 sigma model. The Lie-point symmetries of the CP N−1 model are computed for arbitrary N . The Weierstrass formula for immersion is determined and an explicit formula for a moving frame on a surface is constructed. This allows us ...

Sigma Models and Minimal Surfaces

The correspondance is established between the sigma models , the minimal surfaces and the Monge-Ampére equation. The Lax-Pairs of the minimality condition of the minimal surfaces and the MongeAmpére equations are given. Existance of infinitely many nonlocal conservation laws is shown and some Backlund transformations are also given.

Poisson Sigma Models on Surfaces with Boundary: Classical and Quantum Aspects

Algebraic and Analytic Aspects of Soliton Type Equations

This is a review of two of the fundamental tools for analysis of soliton equations: i) the algebraic ones based on Kac-Moody algebras, their central extensions and their dual algebras which underlie the Hamiltonian structures of the NLEE; ii) the construction of the fundamental analytic solutions (FAS) of the Lax operator and the Riemann-Hilbert problem (RHP) which they satisfy. The fact that t...

Description of surfaces associated with Grassmannian sigma models on Minkowski space

We construct and investigate smooth orientable surfaces in su(N) algebras. The structural equations of surfaces associated with Grassmannian sigma models on Minkowski space are studied using moving frames adapted to the surfaces. The first and second fundamental forms of these surfaces as well as the relations between them as expressed in the Gauss–Weingarten and Gauss–Codazzi–Ricci equations a...