Integrable Structure of Interface Dynamics

Integrable dynamics of coupled Fermi-Bose condensates

Emil A. Yuzbashyan,1 Vadim B. Kuznetsov,2 and Boris L. Altshuler3 1Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA 2Department of Applied Mathematics, University of Leeds Leeds, LS2 9JT, United Kingdom 3Physics Department, Princeton University, Princeton, New Jersey 08544, USA Received 29 June 2005; revised manuscript recei...

Integrable Dynamics of Knotted Vortex Filaments

The dynamics of vortex filaments has provided for almost a century one of the most interesting connections between differential geometry and soliton equations, and an example in which knotted curves arise as solutions of differential equations possessing an infinite family of symmetries and a remarkably rich geometrical structure. These lectures discuss several aspects of the integrable dynamic...

Dynamics of solitons in nearly integrable systems

A detailed survey of the technique of perturbation theory for nearly integrable systems, based upon the inverse scattering transform, and a minute account of results obtained by means of that technique and alternative methods are given. Attention is focused on four classical nonlinear equations: the Korteweg —de Vries, nonlinear Schrodinger, sine-Gordon, and Landau-Lifshitz equations perturbed ...

Integrable structure of modified melting crystal model

Our previous work on a hidden integrable structure of the melting crystal model (the U(1) Nekrasov function) is extended to a modified crystal model. As in the previous case, “shift symmetries” of a quantum torus algebra plays a central role. With the aid of these algebraic relations, the partition function of the modified model is shown to be a tau function of the 2D Toda hierarchy. We conject...

Integrable structure of melting crystal models