 01405 TaiPeng Tsai and HorngTzer Yau
 Stable Directions for Excited States of Nonlinear Schr\"odinger Equations
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Oct 30, 01

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Abstract. 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
nonresonant and resonant cases. In the resonant case, the
linearized operators around the excited states are nonself
adjoint perturbations to some linear Hamiltonians with embedded
eigenvalues. Although selfadjoint perturbation turns embedded
eigenvalues into resonances, this class of nonself 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.
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