Research Interests for Xin Zhou

Professor Zhou studies the 1-D, 2-D inverse scattering theory, using the method of Riemann-Hilbert problems. His current research is concentrated in a nonlinear type of microlocal analysis on Riemann-Hilbert problems. Subjects of main interest are integrable and near intergrable PDE, integrable statistical models, orthogonal polynomials and random matrices, monodromy groups and Painleve equations with applications in physics and algebraic geometry. A number of classical and new problems in analysis, numerical analysis, and physics have been solved by zhou or jointly by zhou and his collaborators.

Recent Publications

1. with A. Tovbis, S. Venakides, On the long time limit of semiclassical (zero dispersion limit) solutions of the focusing Nonlinear Schroedinger Equation: Pure radiation case.,, Comm. Pure Appl. Math. (Accepted, 2006)
2. with K. McLaughlin , A.H. Vartanian, Asymptotics of Orthogonal Laurent Polynomials of Odd Degree with Respect to Varying Exponential Weights, Constructive Approximation (Accepted, 2006)
3. B. Rider and X. Zhou, Janossy densities for unitary ensembles at the spectral edge (Preprint, 2006)
4. with K. T.-R. McLaughlin, A. H. Vartanian, Asymptotics of Coefficients of Recurrence Relations, Hankel Determinants Ratios, and Root Products Associated with Orthogonal Laurent Polynomials with Respect to Varying Exponential Weights, journal Acta Applicandae Mathematicae (Submitted, 2006)
5. with A. Tovbis and S. Venakides, Semiclassical focusing nonlinear Schroedinger equation I: Inverse scattering map and its evolution for radiative initial data, completed (Submitted, 2006)