30 research outputs found
On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth
We review applications of theory of classical and quantum integrable systems
to the free-boundary problems of fluid mechanics as well as to corresponding
problems of statistical mechanics. We also review important exact results
obtained in the theory of multi-fractal spectra of the stochastic models
related to the Laplacian growth: Schramm-Loewner and Levy-Loewner evolutions
A Critical Phenomenon in Solitonic Ising Chains
We discuss a phase transition of the second order taking place in non-local
1D Ising chains generated by specific infinite soliton solutions of the KdV and
BKP equations.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA