Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2009-07-07
Nonlinear Sciences
Exactly Solvable and Integrable Systems
submitted to J. Phys. A: Math. and Theor
Scientific paper
The possibility of the decomposition of the three dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schr\"{o}dinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, solutions of the 3D controlled GPE can be constructed from the solutions of a 2D linear Schr\"{o}dinger equation (transverse component of the GPE) coupled with a 1D nonlinear Schr\"{o}dinger equation (longitudinal component of the GPE). Such a decomposition, called the 'controlling potential method' (CPM), allows one to cast the above solutions in the form of the product of the solutions of the transverse and the longitudinal components of the GPE. The coupling between these two equations is the functional of both the transverse and the longitudinal profiles. The analysis shows that the CPM is based on the variational principle that sets up a condition on the controlling potential well, and whose physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control operation.
de Nicola Sergio
Eliasson Bengt
Fedele Renato
Jovanovic Dusan
Kant Shukla Padma
No associations
LandOfFree
Some mathematical aspects in determining the 3D controlled solutions of the Gross-Pitaevskii equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Some mathematical aspects in determining the 3D controlled solutions of the Gross-Pitaevskii equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some mathematical aspects in determining the 3D controlled solutions of the Gross-Pitaevskii equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-356372