Necklace-ring solitons have gained much attention due to their potential applications in optics and other scientific areas. In this paper, the numerical investigation of the nonlinear Schrödinger equation by using the curvilinear coordinate lattice Boltzmann method is proposed to study necklace-ring solitons. Different from those used in the general curvilinear coordinate lattice Boltzmann models, the lattices used in this work are uniform in two- and three-dimensional space. Furthermore, the model contains spatial evolution rather than time evolution to avoid the complexity of dealing with higher-order time derivative terms as well as to maintain the simplicity of the algorithm. Numerical experiments reproduce the evolution of two- and three-dimensional necklace-ring solitons. The truncation error analysis indicates that our model is equivalent to the Crank–Nicolson difference scheme.

中文翻译：

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非线性薛定谔方程中项链环梁的曲线坐标格子玻尔兹曼模拟

项链环孤子因其在光学和其他科学领域的潜在应用而备受关注。本文提出了利用曲线坐标格子Boltzmann方法对非线性薛定谔方程进行数值研究来研究项链-环孤子。与一般曲线坐标格子玻尔兹曼模型中使用的格子不同，本工作中使用的格子在二维和三维空间中是均匀的。此外，该模型包含空间演化而不是时间演化，以避免处理高阶时间导数项的复杂性以及保持算法的简单性。数值实验再现了二维和三维项链环孤子的演化。