This paper studies the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation. The first integral of this equation, the phase portraits and the effective potentials are provided. Two different methods are applied to find exact analytical solutions. These methods are the arbitrary nonlinear parameters and the new Jacobi elliptic function expansion method. To give a behavior of the equation studied, some representations are done. In the context of mono-mode optical fibers and in many other domains like nonlinear transmission lines, Bose-Einstein capacitors and so on, the results obtained may be used. We have also established that the solutions obtained here are different from those encounter in the literature concerning the same model.

本文研究（2 + 1）维双曲非线性Schrödinger方程。提供该方程式的第一积分，相图和有效电势。应用两种不同的方法来找到精确的分析解决方案。这些方法是任意非线性参数和新的Jacobi椭圆函数展开方法。为了给出所研究方程的行为，做了一些表示。在单模光纤的背景下以及在许多其他领域（如非线性传输线，Bose-Einstein电容器等）中，可以使用获得的结果。我们还确定，此处获得的解决方案与文献中有关同一模型的解决方案不同。