Tsai, Tai-PengYau, Horng-Tzer2017-05-182002Tsai, Tai-Peng, and Horng-Tzer Yau. 2002. "Relaxation of excited states in nonlinear Schrödinger equations." International Mathematics Research Notices 2002, no. 31: 1629-1673.1073-7928http://nrs.harvard.edu/urn-3:HUL.InstRepos:32706719We consider a nonlinear Schrödinger equation with a bounded local potential in ℝ3. The linear Hamiltonian is assumed to have two bound states with the eigenvalues satisfying some resonance condition. Suppose that the initial data is small and is near some nonlinear excited state. We give a sufficient condition on the initial data so that the solution to the Schrödinger equation approaches to certain nonlinear ground state as the time tends to infinity. Our proof is based on a notion of outgoing estimate which measures the time-direction related information of the wave functions for the nonlinear Schrödinger equations.en-USJournal Article2017-05-1810.1155/S1073792802201063