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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.

自1995年在碱金属气体中发现玻色-爱因斯坦凝聚态以来，BEC和原子激光的材料特性得到了深入研究。 BEC 中的非线性动力学也得到了深入研究。在旋转的 BEC 中发现了量子涡旋和涡旋晶格。在被外部磁场限制在一维空间的 BEC 中发现了孤子和暗孤子。这些非线性激励可以用Gross-Pitaevskii方程或非线性薛定谔方程很好地描述。我们对外势下的非线性薛定谔方程和空间调制非线性薛定谔方程进行了数值研究，发现了一些关于孤子和涡旋的新结果。我们的研究成果发表在Physical Review等杂志上。通过多束激光的干涉，我们可以引入空间周期性势，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。部分研究结果如下： 1．研究了方形光学晶格中孤子晶格和涡旋晶格的稳定性。 2．我们证明了带隙孤子在准周期光学晶格中稳定存在。 3．研究了旋转光学晶格中孤子的稳定性。 4．研究了具有空间调制非线性的一维非线性薛定谔方程中的孤子运动。 5．我们在具有空间调制非线性的非线性薛定谔方程中发现了稳定的二维孤子。6．我们发现了一些自然产生二维暗孤子的过程。7．我们在无粘性的复Ginzburg-Landau方程中发现了任意速度的运动孤子和涡旋，并研究了它们之间的碰撞。