Rationale

The nonlinear Schroedinger and quantum Boltzmann equations are the starting point of applied sciences like quantum mechanics, chemistry, statistical physics, astrophysics, plasma physics, and so on, in the description of transport theory and nonlinear wave phenomena of particles such as propagation of a laser beam, motion of water wave at the free surface of an ideal fluid, plasma waves, a binary signal through optical fibers, dynamics of a rarefied gas, charge transport in ultra-small electronic devices; as well as the Bose-Einstein condensation (BEC)--a phenomena where cold atoms ensemble one particle quantum state in a dilute gas. In the last two decades there are enormous amount of contribution on the mathematical analysis, numerical simulation and applications of the nonlinear Schroedinger and quantum Boltzmann equations. In this minisymposium, the speakers will address the recent progress in the following directions:

(i). Mathematical analysis on existence, stability, and asymptotic behavior of the nonlinear Schroedinger and quantum Boltzmann equations; Semiclassical analysis of the Schroedinger-related equations and their quantum hydrodynamics;

(ii). Numerical methods for the nonlinear Schroedinger and quantum Boltzmann equations including time-splitting spectral methods, symplectic finite difference method, adaptive refinement for capturing blowup and absorbing boundary conditions; numerical simulation for BEC; quantized vortex states and dynamics in superconductivity and superfluidity; and

(iii) Applications to nonlinear optics, semiconductor, plasma physics and dilute gas etc.

Program