Lattice Boltzmann schemes for the nonlinear Schrödinger equation

Ping Dong, Shide Feng, Shouting Gao, Linhao Zhong

    Research output: Contribution to journalArticle

    39 Citations (Scopus)

    Abstract

    The lattice Boltzmann (LB) method is applied to solve the time-dependent nonlinear Schrödinger (NLS) equation. Through approximating the reaction term at different orders of accuracy, three diffusion-reaction LB schemes are constructed for the cubic NLS equation. A LB initial condition is proposed to include the first-order nonequilibrium distribution function. These LB schemes are used to solve the one-soliton propagation and the homoclinic orbit problems. Detailed simulation results confirm that the high-order reaction term and the LB initial condition are effective in reducing the truncation errors. Compared with the Crank-Nicolson finite difference scheme, the LB scheme is found to give at least comparable and generally more accurate approximation for the cubic NLS equation.
    Original languageEnglish
    Article numberARTN 036704
    Number of pages9
    JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
    Volume74
    Issue number3
    DOIs
    Publication statusPublished - 2006

    Keywords

    • ROSSBY SOLITON MODEL
    • QUANTUM-MECHANICS
    • WAVES
    • CELLULAR-AUTOMATA
    • BLOCK-EDDY INTERACTION
    • GAS MODEL

    Fingerprint Dive into the research topics of 'Lattice Boltzmann schemes for the nonlinear Schrödinger equation'. Together they form a unique fingerprint.

  • Cite this