SWtools: A Python package implementing iterative solvers for soliton solutions of nonlinear Schrödinger-type equations

Solitons are ubiquitous in nature and play a pivotal role in the structure and dynamics of solutions of nonlinear propagation equations. In many instances where solitons are expected to exist, analytical expressions of these special objects are not available. The presented software fills this gap, allowing users to numerically calculate soliton solutions for a generic nonlinear Schrödinger-type equation by iteratively solving an associated nonlinear eigenvalue problem. The package implements a range of methods, including the spectral renormalization method, and a relaxation method for the problem with additional normalization constraint. We verify the implemented methods in terms of a problem for which an analytical soliton expression is available, and demonstrate the implemented functionality by numerical experiments for example problems in nonlinear optics and matter-wave solitons in quantum mechanics. For common variants of the considered equation, SWtools also implements functions retrieving linear stability eigenvalues and modes for its solitons. The presented Python package is open-source and released under the MIT License in a publicly available software repository.

孤子（Solitons）在自然界中无处不在，且在非线性传播方程解的结构与动力学特性中发挥着关键作用。在诸多预期存在孤子的场景中，这类特殊非线性结构的解析表达式往往难以获取。本软件填补了这一空白，支持用户通过迭代求解相关联的非线性本征值问题，对通用的非线性薛定谔型方程（nonlinear Schrödinger-type equation）进行数值计算以获取其孤子解。该软件包实现了多种求解方法，包括光谱重整化法，以及针对带有额外归一化约束问题的松弛法。我们通过一个存在解析孤子解的基准问题验证了所实现方法的正确性，并通过非线性光学领域的示例问题以及量子力学中的物质波孤子相关数值实验，展示了该软件包的功能。针对所研究方程的常见变体，SWtools还实现了用于提取其孤子线性稳定性本征值与本征模式的功能。本开源Python软件包采用MIT许可证发布，并托管于公开软件仓库中。