IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3807-d1534516.html
   My bibliography  Save this article

Numerical Simulation for the Wave of the Variable Coefficient Nonlinear Schrödinger Equation Based on the Lattice Boltzmann Method

Author

Listed:
  • Huimin Wang

    (College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China)

  • Hengjia Chen

    (College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China)

  • Ting Li

    (College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China)

Abstract

The variable coefficient nonlinear Schrödinger equation has a wide range of applications in various research fields. This work focuses on the wave propagation based on the variable coefficient nonlinear Schrödinger equation and the variable coefficient fractional order nonlinear Schrödinger equation. Due to the great challenge of accurately solving such problems, this work considers numerical simulation research on this type of problem. We innovatively consider using a mesoscopic numerical method, the lattice Boltzmann method, to study this type of problem, constructing lattice Boltzmann models for these two types of equations, and conducting numerical simulations of wave propagation. Error analysis was conducted on the model, and the convergence of the model was numerical validated. By comparing it with other classic schemes, the effectiveness of the model has been verified. The results indicate that lattice Boltzmann method has demonstrated advantages in both computational accuracy and time consumption. This study has positive significance for the fields of applied mathematics, nonlinear optics, and computational fluid dynamics.

Suggested Citation

  • Huimin Wang & Hengjia Chen & Ting Li, 2024. "Numerical Simulation for the Wave of the Variable Coefficient Nonlinear Schrödinger Equation Based on the Lattice Boltzmann Method," Mathematics, MDPI, vol. 12(23), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3807-:d:1534516
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3807/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/23/3807/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yu, Fajun & Li, Li, 2024. "Soliton robustness, interaction and stability for a variable coefficients Schrödinger(VCNLS) equation with inverse scattering transformation," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    2. Wang, Huimin, 2016. "A lattice Boltzmann model for the ion- and electron-acoustic solitary waves in beam-plasma system," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 62-75.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huimin Wang & Yanhong Liu & Xiuling Li & Hengjia Chen, 2024. "Numerical Simulation for Solitary Waves of the Generalized Zakharov Equation Based on the Lattice Boltzmann Method," Mathematics, MDPI, vol. 12(7), pages 1-14, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3807-:d:1534516. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.