Curvilinear coordinate lattice Boltzmann simulation for necklace-ring beams in the nonlinear Schrödinger equation

Boyu Wang, Jianying Zhang () and Guangwu Yan ()
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Boyu Wang: College of Mathematics, Jilin University, Changchun 130012, P. R. China
Jianying Zhang: #x2020;School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, P. R. China
Guangwu Yan: College of Mathematics, Jilin University, Changchun 130012, P. R. China

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 10, 1-15

Abstract: 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.

Keywords: Nonlinear Schrödinger equation; lattice Boltzmann method; curvilinear coordinate; necklace-ring solitons (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120501363

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