Physics – Mathematical Physics
Scientific paper
2001-10-31
Physics
Mathematical Physics
v2: sec 3 changed
Scientific paper
We consider nonlinear Schr\"odinger equations in $\R^3$. Assume that the linear Hamiltonians have two bound states. For certain finite codimension subset in the space of initial data, we construct solutions converging to the excited states in both non-resonant and resonant cases. In the resonant case, the linearized operators around the excited states are non-self adjoint perturbations to some linear Hamiltonians with embedded eigenvalues. Although self-adjoint perturbation turns embedded eigenvalues into resonances, this class of non-self adjoint perturbations turn an embedded eigenvalue into two eigenvalues with the distance to the continuous spectrum given to the leading order by the Fermi golden rule.
Tsai Tai-Peng
Yau Horng-Tzer
No associations
LandOfFree
Stable Directions for Excited States of Nonlinear Schrödinger Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stable Directions for Excited States of Nonlinear Schrödinger Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stable Directions for Excited States of Nonlinear Schrödinger Equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-105076