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arXiv · 2504.10623

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

O. Melchert·A. Demircan
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Abstract

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 exist, analytical expressions of these special objects are not available. The presented software fills this gap, allowing users to numerically calculate soliton solutions for nonlinear Schrödinger-type equations by iteratively solving an associated nonlinear eigenvalue problem. The package implements a range of methods, including the spectral renormalization method (SRM), and a relaxation method for the problem with additional normalization constraint (NSOM). 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. The presented Python package is open-source and released under the MIT License in a publicly available software repository (https://github.com/omelchert/SWtools).

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BibTeXRIS

O. Melchert, A. Demircan. 2025-04-14. SWtools: A Python module implementing iterative solvers for soliton solutions of nonlinear Schrödinger-type equations. https://arxiv.org/abs/2504.10623

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