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学术报告---林太家

2018-09-03 08:05:58 来源:华南师范大学华南数学应用与交叉研究中心 点击: 收藏本文

学术报告


         题      目:Energe and elgenvalue estimates of ground states of coupled nonlinear Schrödinger equation


         报  告  人: 林太家 教授  

                     台湾大学


         邀  请  人:丁时进  教授


         时      间:2018-09-04 15:30--16:30


         地      点:学术报告厅111



摘      要:

      

   Coupled nonlinear Schrödinger(NLS) equations with trap potentials and cubic nonlinearrities (which describe repulsive intraspecies and interspecies interacitons) have become a fundamental model of superfluids and Bose-Einstein condensates. The ground state of the coupled NLS equations under the L2 norm normalization conditions. Generically, the ground state of the coupled NLS equations satisfies an eigenvalue problem of a nonlinear elliptic system which has no general theory for the energy and eigenvalue estimates. Using the energy  and eigenvalues of the ground state of the coupled NLS equations as parameter  I  goes to infinity which represents trap potentials tend to zero. Furthermore, the asymptotic behaviors of the energy and eigenvalues of the ground state are of order I--a, where  0<a<1 depends on the spatial dimension and the degrees of trap potentials.