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The evolution process of the solutions for the coupled nonlinear Schrödinger equations via Fourier neural operator approach

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  • Ren, Hong-Mei
  • Tian, Shou-Fu

Abstract

In this work, the Fourier neural operator (FNO) method is developed to the coupling system for the first time to investigate the data-driven solutions of the coupled nonlinear Schrödinger equations. For the coupled nonlinear Schrödinger equation (CNLS) equation, we successfully establish the mapping between the initial conditions and the rational solutions. Simultaneously, the FNO learning method is utilized to investigate the transformation process of the rogue, Ma breather and Akhmediev breather solutions of the coupled generalized nonlinear Schrödinger (CGNLS) equation. By comparing the data-driven solution with the exact solution, we can find that the FNO network can perform well in all cases even though these solution parameters have strong influences on the wave structures. Finally, we explore the influences of different activation functions and Fourier layers on the performance of the algorithm to test the characterization ability of FNO. The results obtained in this paper can be used to further explore coupled nonlinear Schrödinger equations and the applications of deep learning method in the coupled system.

Suggested Citation

  • Ren, Hong-Mei & Tian, Shou-Fu, 2026. "The evolution process of the solutions for the coupled nonlinear Schrödinger equations via Fourier neural operator approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 1082-1096.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:1082-1096
    DOI: 10.1016/j.matcom.2025.07.059
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