NonlinearSchrodinger.jl is a Julia package with a simple interface for studying solutions of nonlinear Schr\"odinger equations (NLSEs). In approximately ten lines of code, one can perform a simulation of the cubic NLSE using one of 32 algorithms, including symplectic and Runge-Kutta-Nystr\"om integrators up to eighth order. Furthermore, it is possible to compute analytical solutions via a numerical implementation of the Darboux transformation for extended NLSEs up to fifth order, with an equally simple interface. In what follows, we review the fundamentals of solving this class of equations numerically and analytically, discuss the implementation, and provide several examples.

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NonlinearSchrodinger：非线性Schrödinger方程的高阶算法和Darboux变换

NonlinearSchrodinger.jl是一个具有简单接口的Julia软件包，用于研究非线性Schr“ odinger方程（NLSE）的解决方案。在大约十行代码中，可以使用32种算法（包括辛算法和Runge-Kutta-Nystr \ om积分器最多八阶。此外，还可以通过Darboux变换的数值实现，使用同样简单的界面，将扩展的NLSE扩展到五阶，从而计算出解析解。在下文中，我们回顾了用数值和分析方法解决此类方程式的基础知识，讨论了实现方法，并提供了一些示例。