Abstract
We calculate the Lax pairs of homogeneous and inhomogeneous one-dimensional time-dependent Gross-Pitaevskii equations with time-dependent scattering length. The inhomogeneity corresponds to linear and quadratic potentials. Our approach introduces a systematic method of searching for the Lax pair corresponding to a given differential equation. We derive known Lax pairs for the Gross-Pitaevskii equation with homogeneous and quadratic potentials and time-dependent scattering length. We also derive new Lax pairs corresponding to a Gross-Pitaevskii equation with a linear potential. Using the resulting Lax pairs, the Darboux transformation can be performed and exact solutions of the Gross-Pitaevskii equation can be obtained for experimentally relevant cases such as solitonic solutions.
| Original language | English |
|---|---|
| Article number | 002 |
| Pages (from-to) | 9679-9691 |
| Number of pages | 13 |
| Journal | Journal of Physics A: Mathematical and General |
| Volume | 39 |
| Issue number | 31 |
| DOIs | |
| Publication status | Published - Aug 4 2006 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)