A discrete model governing a system of cold bosonic atoms in zig-zag optical lattices in quantum optics was proposed in the literature. In an analog to this model, a continuum model is, here constructed. The resulting equation is a nonlinear Schrodinger equation NLSE with drift force and linear growth. Exact solutions of this equation are obtained. To this issue, a new transformation that allows to inspect the optical lattice due to soliton–periodic wave collision is introduced. Here, the colliding dynamics are inspected. A class of polynomial and rational solutions of the model equation constructed are obtained by using the unified and generalized unified methods. The solutions found reveal the propagation of local zigzag-shaped pulses in optical lattices. Mixed smooth–sharp (shock-like) optical pulses are also observed. This leads to the issue that the collision is locally elastic (or inelastic). Furthermore, self-modulation zigzag-shaped pulses with compression, are remarked. We mention that the zigzag-shaped pulses, in an optical lattice, was not found in the literature. Thus, the results found in this work are original. It is found that the polarization of zig-zag optical lattice is self-focusing.

文献中提出了一种离散模型，用于控制量子光学中锯齿形光学晶格中的冷玻色原子系统。与该模型类似，这里构建了一个连续模型。由此产生的方程是一个非线性薛定谔方程NLSE，具有漂移力和线性增长。得到这个方程的精确解。针对这个问题，引入了一种新的变换，可以检查由于孤子-周期波碰撞引起的光学晶格。在这里，检查碰撞动力学。使用统一方法和广义统一方法，得到所构造模型方程的一类多项式和有理解。发现的解决方案揭示了局部锯齿形脉冲在光学晶格中的传播。还观察到混合的平滑-尖锐（冲击状）光脉冲。这导致碰撞是局部弹性（或非弹性）的问题。此外，还提到了带有压缩的自调制锯齿形脉冲。我们提到在文献中没有发现光学晶格中的锯齿形脉冲。因此，在这项工作中发现的结果是原始的。发现锯齿形光学晶格的偏振是自聚焦的。