Motion of nonlinear Schroedinger solitons under external potentials

外部电势下非线性薛定谔孤子的运动

基本信息

批准号：
17540358
负责人：
SAKAGUCHI Hidetsugu
金额：
$ 1.66万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

项目摘要

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.

由于在1995年在碱金属气体中发现了玻色的凝结物，因此对BEC和原子激光的材料特性进行了深入研究。还深入研究了BEC中的非线性动力学。在旋转BEC中发现了量子涡流和涡流晶格。在外部磁场限制在一维空间中的BEC中发现了孤子和深色孤子。这些非线性激发由Gross-Pitaevskii方程或非线性Schroedinger方程很好地描述。我们在外部电势和空间调制的非线性Schroedingher方程下数值研究了非线性Schroedinger方程，并找到了Solitons and Solitons and solitons and vortices and vortices。我们已经在物理审查中发表了结果，依此类推。通过几个激光灯的干扰，我们可以引入空间周期电势，这称为光学晶格。在各种光学晶格中，孤子和涡旋表现出各种运动。以下结果指出了一些结果。1。我们研究了在正方形光晶格中孤子晶格和涡旋晶格的稳定性。2。我们已经表明，间隙孤子稳定存在于准碘光学晶格中3。我们研究了旋转光晶格中孤子的稳定性4。我们已经研究了具有空间调节的非线性的一维非线性schroedinger方程中的单齿运动。5。我们在非线性Schroedinger方程中发现了一个稳定的二维孤子，其空间调制了非线性6。我们发现了一些自然创建二维暗孤子的过程。7。我们已经发现，在复杂的金兹堡 - 兰道方程中，孤子和涡流没有粘度，并研究了相互碰撞。