Published February 28, 2017
| Submitted
Journal Article
Open
Adiabatic theorem for the Gross–Pitaevskii equation
- Creators
- Gang, Zhou
- Grech, Philip
Abstract
We prove an adiabatic theorem for the nonautonomous semilinear Gross–Pitaevskii equation. More precisely, we assume that the external potential decays suitably at infinity and the linear Schrödinger operator −Δ+V_s admits exactly one bound state, which is ground state, for any s∈[0,1]. In the nonlinear setting, the ground state bifurcates into a manifold of (small) ground state solutions. We show that, if the initial condition is at the ground state manifold, bifurcated from the ground state of −Δ+V_0, then, for any fixed s∈[0,1], as ε→0, the solution will converge to the ground state manifold bifurcated from the ground state of −Δ+V_s. Moreover, the limit is of the same mass to the initial condition.
Additional Information
© 2017 Taylor & Francis. Partly supported by NSF grant DMS-1308985 and DMS-1443225.Attached Files
Submitted - 1508.02351.pdf
Files
1508.02351.pdf
Files
(348.9 kB)
Name | Size | Download all |
---|---|---|
md5:5f558b72c83bca3bd204f5cb6b30cdef
|
348.9 kB | Preview Download |
Additional details
- Eprint ID
- 77748
- Resolver ID
- CaltechAUTHORS:20170525-080748355
- DMS-1308985
- NSF
- DMS-1443225
- NSF
- Created
-
2017-05-25Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field