NonlinearSchrodinger：非线性薛定谔方程的高阶算法和达布变换
NonlinearSchrodinger: Higher-Order Algorithms and Darboux Transformations for Nonlinear Schrödinger Equations
摘要：
NonlinearSchrodinger.jl是一个Julia软件包，具有简单的界面，用于研究非线性薛定谔方程（NLSE）的解。在大约10行代码中，可以使用32种算法之一来执行立方NLSE的模拟，包括辛和Runge-Kutta-Nyström积分器，最高可达八阶。此外，它是可能的，通过数值实现的达布变换的扩展NLSE五阶，具有同样简单的接口，计算分析解决方案。在下文中，我们将回顾用数值和解析方法求解这类方程的基本原理，讨论实现方法，并提供几个例子。
英文摘要：
NonlinearSchrodinger.jl is a Julia package with a simple interface for studying solutions of nonlinear Schrödinger 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-Nyström 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
