In this paper, using the continuum approximation and from a discrete equation governing a system of cold bosonic atoms in zig-zag optical lattices derived an equation in a continuum domain. With two different methods, namely the $$exp_a$$ e x p a function method and the Hyperbolic function method, found many solutions of the equation considered. These solutions are Hyperbolic solutions and trigonometric solutions. Discrete representations have been done to observe their behaviors. These results will help to understand the dynamics of cold bosonic atoms in zig-zag optical lattices and several other systems. More importantly, in this article derived the Lagrangian and the stability condition of the model studied. The methods employed here are very simple and concise.

中文翻译：

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锯齿形光学晶格中冷玻色原子的光学解

在本文中，使用连续谱近似并从控制之字形光学晶格中冷玻色原子系统的离散方程推导出连续域中的方程。用两种不同的方法，即$$exp_a$$ expa 函数法和双曲函数法，找到了所考虑方程的许多解。这些解是双曲解和三角解。已经进行了离散表示来观察他们的行为。这些结果将有助于了解锯齿形光学晶格和其他几个系统中冷玻色子原子的动力学。更重要的是，本文推导了所研究模型的拉格朗日函数和稳定性条件。这里采用的方法非常简单和简洁。