Asymptotic Dynamics of Nonlinear Schrodinger Equations: Resonance Dominated and Radiation Dominated Solutions
Tsai, Tai-Peng ; Yau, Horng-Tzer
arXiv, 0011036 / Harvested from arXiv
Text on arXiv
We consider a linear Schr\"odinger equation with a small nonlinear perturbation in $R^3$. Assume that the linear Hamiltonian has exactly two bound states and its eigenvalues satisfy some resonance condition. We prove that if the initial data 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 Schr\"odinger equation and its asymptotic profile can have two different types of decay: 1. The resonance dominated solutions decay as $t^{-1/2}$. 2. The radiation dominated solutions decay at least like $t^{-3/2}$.
Publié le : 2000-11-21
Classification:  Mathematical Physics,  Mathematics - Analysis of PDEs 
@article{0011036,
     author = {Tsai, Tai-Peng and Yau, Horng-Tzer},
     title = {Asymptotic Dynamics of Nonlinear Schrodinger Equations: Resonance
  Dominated and Radiation Dominated Solutions},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0011036}
}

Tsai, Tai-Peng; Yau, Horng-Tzer. Asymptotic Dynamics of Nonlinear Schrodinger Equations: Resonance
  Dominated and Radiation Dominated Solutions. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0011036/