学术讲座 Lecture

   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.