2006 Fiscal Year Final Research Report Summary
Motion of nonlinear Schroedinger solitons under external potentials
| Project/Area Number |
17540358
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyushu University |
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Principal Investigator |
SAKAGUCHI Hidetsugu Kyushu University, Faculty of Engineering Sciences, Associate Professor, 総合理工学研究院, 助教授 (90192591)
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| Project Period (FY) |
2005 – 2006
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| Keywords | soliton / vortex / Bose condensation / nonlinear Schroedinger equation / optical lattice |
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| Research Abstract |
Since Bose-Einstein condensates were found in alkali metal gases in 1995, material properties of BECs and atomic laser have been intensively studied. Nonlinear dynamics in BECs is also intensively studied. Quantum vortices and vortex lattices were found in rotating BECs. Solitons and dark solitons were found in BECs confined in one dimensional space by external magnetic field. These nonlinear excitation is well described by the Gross-Pitaevskii equation or the nonlinear Schroedinger equation.
We have numerically studied the nonlinear Schroedinger equation under external potential and the spatially modulated nonlinear Schroedingher equation, and found some new results concerning the solitons and the vortices. We have published the results in Physical Review and so on. By the interference of several laser lights, we can introduce spatially periodic potentials, which are called optical lattices. In various optical lattices, solitons and vortices exhibit various motion. Some results are pointed out in the followings.
1. We have studied the stability of soliton lattices and vortex lattices in a square optical lattice.
2. We have shown that gap solitons exist stably in a quasiperiodic optical lattice.
3. We have studied the stability of solitons in a rotating optical lattice.
4. We have studied soliton motions in the one-dimensional nonlinear Schroedinger equation with spatially modulated nonlinearity.
5. We have found a stable two-dimensional soliton in the nonlinear Schroedinger equation with spatially moduated nonlinearity.
6. We have found some processes in which two-dimensional dark solitons are naturally created.
7. We have found moving solitons and vortices with arbitrary velocities in the complex Ginzburg-Landau equation without viscosity, and studied the mutual collision.
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Research Products
(14 results)
