Uniform semiclassical approximations of the nonlinear Schroedinger equation by a Painleve mapping
| dc.creator | Witthaut, D. | |
| dc.creator | Korsch, H. J. | |
| dc.date | 2006-08-11 | |
| dc.date.accessioned | 2026-07-07T09:56:05Z | |
| dc.date.available | 2026-07-07T09:56:05Z | |
| dc.description | A useful semiclassical method to calculate eigenfunctions of the Schroedinger equation is the mapping to a well-known ordinary differential equation, as for example Airy's equation. In this paper we generalize the mapping procedure to the nonlinear Schroedinger equation or Gross-Pitaevskii equation describing the macroscopic wave function of a Bose-Einstein condensate. The nonlinear Schroedinger equation is mapped to the second Painleve equation, which is one of the best-known differential equations with a cubic nonlinearity. A quantization condition is derived from the connection formulae of these functions. Comparison with numerically exact results for a harmonic trap demonstrates the benefit of the mapping method. Finally we discuss the influence of a shallow periodic potential on bright soliton solutions by a mapping to a constant potential. | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0608099 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0608099 | |
| dc.identifier | J. Phys. A: Math. Gen. 39, 14687 (2006) | |
| dc.identifier | doi:10.1088/0305-4470/39/47/012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166856 | |
| dc.subject | Quantum Physics | |
| dc.title | Uniform semiclassical approximations of the nonlinear Schroedinger equation by a Painleve mapping | |
| dc.type | text |