| Contents |
| I will first summarize a rigorous theory on existence of bifurcation points for ground states and excited states of nonlinear Schr\"{o}dinger/Gross-Pitaevskii equations in both weakly and strongly nonlinear regimes. A few particular cases where all bifurcation points can be found will also be presented. Then I will discuss dynamical properties of solutions starting near the bifurcation points, including the orbital and asymptotic stability of the bound state branches emerging from the bifurcation point. The first part is joint work with V. Natarajan (Tel Aviv U.). |
|