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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Boyu Wang & Jianying Zhang & Guangwu Yan, 2020. "Curvilinear coordinate lattice Boltzmann simulation for necklace-ring beams in the nonlinear Schrödinger equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-15, October.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:10:n:s0129183120501363
    DOI: 10.1142/S0129183120501363
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