-
- A. SOFFER
- Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA
-
- M. I. WEINSTEIN
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
書誌事項
- 公開日
- 2004-09
- DOI
-
- 10.1142/s0129055x04002175
- 公開者
- World Scientific Pub Co Pte Lt
この論文をさがす
説明
<jats:p> We prove for a class of nonlinear Schrödinger systems (NLS) having two nonlinear bound states that the (generic) large time behavior is characterized by decay of the excited state, asymptotic approach to the nonlinear ground state and dispersive radiation. Our analysis elucidates the mechanism through which initial conditions which are very near the excited state branch evolve into a (nonlinear) ground state, a phenomenon known as ground state selection. Key steps in the analysis are the introduction of a particular linearization and the derivation of a normal form which reflects the dynamics on all time scales and yields, in particular, nonlinear master equations. Then, a novel multiple time scale dynamic stability theory is developed. Consequently, we give a detailed description of the asymptotic behavior of the two bound state NLS for all small initial data. The methods are general and can be extended to treat NLS with more than two bound states and more general nonlinearities including those of Hartree–Fock type. </jats:p>
収録刊行物
-
- Reviews in Mathematical Physics
-
Reviews in Mathematical Physics 16 (08), 977-1071, 2004-09
World Scientific Pub Co Pte Lt
