IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v192y2025ics0960077924014954.html
   My bibliography  Save this article

Analysis of neural network methods for obtaining soliton solutions of the nonlinear Schrödinger equation

Author

Listed:
  • Moloshnikov, Ivan A.
  • Sboev, Alexander G.
  • Kutukov, Aleksandr A.
  • Rybka, Roman B.
  • Kuvakin, Mikhail S.
  • Fedorov, Oleg O.
  • Zavertyaev, Saveliy V.

Abstract

The paper addresses the practically significant problem of transmitting signals through nonlinear optical media by solving generalized nonlinear Schrödinger equations using various modifications of Physics-Informed Neural Networks (PINNs). The study provides numerical soliton solutions for Schrödinger equations of the order as high as four. To tackle this problem, the paper compares segmental modifications of PINNs, including BC-PINNs, FB-PINNs, and MoE-PINNs. Additionally, an adaptive option for selecting collocation points is proposed and explored. The efficiency of the numerical solutions is evaluated using three approaches: comparison with the precise analytical solutions, and two metrics based on conservation laws. The results show that the modified segmentation approach, combined with the developed adaptive selection of collocation points, greatly improves the accuracy and the convergence of PINNs compared to the initial version of the method. On such example problems as the interaction of a soliton with a Gaussian function, two solitons interaction, and the solution of a 4th-order equation, the proposed method demonstrates improved convergence of the numerical solution.

Suggested Citation

  • Moloshnikov, Ivan A. & Sboev, Alexander G. & Kutukov, Aleksandr A. & Rybka, Roman B. & Kuvakin, Mikhail S. & Fedorov, Oleg O. & Zavertyaev, Saveliy V., 2025. "Analysis of neural network methods for obtaining soliton solutions of the nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
  • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077924014954
    DOI: 10.1016/j.chaos.2024.115943
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924014954
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2024.115943?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:eee:chsofr:v:192:y:2025:i:c:s0960077924014954. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.