中文摘要：

我们与另外的限制在一个周期的光潜力为 Bose 爱因斯坦冷凝物(BEC ) 学习静止、繁殖的答案光或磁性的潜力。用有效集体近似，我们以慢慢地变化的信封 modulating 表示冷凝物波浪功能光格子的 Bloch 模式。在弱非线性的限制，我们为不包含格子的快速的摆动的信封功能的繁殖导出一个非线性的 Schrödinger 方程。我们然后在弱、中等、强壮的非线性的相互作用的政体详细考虑扎根的州的答案。我们描述在每政体适当的答案的形式，并且把小心的限制放在答案的每种类型的有效性上。最后，我们扩大学习到旋量的宣传动力学在一个光格子和一些有趣的现象的原子 BEC 被揭示。

英文摘要：

We study the stationary and propagating solutions for a Bose-Einstein condensate （BEC） in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate wave function in terms of slowly-varying envelopes modulating the Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we derive a nonlinear Schrodinger equation for propagation of the envelope function which does not contain the rapid oscillation of the lattice. We then consider the ground state solutions in detail in the regime of weak, moderate and strong nonlinear interactions. We describe the form of solution which is appropriate in each regime, and place careful limits on the validity of each type of solution. Finally we extend the study to the propagating dynamics of a spinor atomic BEC in an optical lattice and some interesting phenomena are revealed.