The ground state and the virial theorem of 2D nonlinear Schrodinger equations with square-root nonlinearity
主 题: The ground state and the virial theorem of 2D nonlinear Schrodinger equations with square-root nonlinearity
报告人: 林太家 (台湾大学数学系)
时 间: 2015-03-19 09:30 - 10:30
地 点: 理科一号楼 1418
Nonlinear Schr?dinger (NLS) equation, a nonlinear variation of the Schr?dinger equation, is a fundamental model for several materials including nonlinear optical mediums and Bose-Einstein condensates. Because two-dimensional (2D) nonlinear Schr?dinger (NLS) equations are non-integrable, there exists no mathematically rigorous theory that would guarantee the general existence of ground state (the energy minimizer under the L2-normalization condition). In this lecture, the existence of ground state in 2D NLS equations with square-root nonlinearity will be introduced. Using the L2-normalization condition, we transform the energy functional suitably so the energy estimate method is applicable to prove the existence of ground state. For all bound states, we use the Pohozaev identity to estimate the ratio of the total kinetic energy and the total potential energy and develop the virial theorem of 2D NLS equations with square-root nonlinearity.
