Asymptotic dynamics of nonlinear Schrödinger equations: Resonance‐dominated and dispersion‐dominated solutions
By Tai-Peng Tsai, Horng-Tzer Yau. 2002
139 citations recorded by the source corpus.
We consider a linear Schrödinger equation with a nonlinear perturbation in ℝ3. Assume that the linear Hamiltonian has exactly two bound states and its eigen‐values satisfy some resonance condition. We prove that if the initial data is sufficiently small and is near a nonlinear ground state, then the solution approaches to certain nonlinear ground state as the time tends to infinity. Furthermore, the difference between the wave function solving the nonlinear Schrödinger equation and its asymptotic profile can have two different types of decay: The resonance‐dominated solutions decay as t−1/2 or the dispersion‐dominated solutions decay at least like t−3/2. © 2002 John Wiley & Sons, Inc.
Subfields: Mathematical Physics, Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/57d03d9db3c7d0f91421c25ce890c6d7ff629349
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In Mathematical Physics
In Numerical Analysis
In Statistical and Nonlinear Physics
Citations in the corpus
- Selection of the ground state for nonlinear schrödinger equations (2003, result): “[ 48 , 49]. Similar results to those of Theorem 1.1 are considered in [51].”
- Solitary Wave Dynamics in an External Potential (2003, result): “The first result of this type was proved by Fröhlich, Tsai and Yau [16, 17] for the Hartree equation ((1.1) with (1.3)) under a spectral condition (see Condition (F) of Section 2).”