Physics-Informed Neural Networks for Higher-Order Nonlinear Schrödinger Equations: Soliton Dynamics in External Potentials

Leonid Serkin () and Tatyana L. Belyaeva ()
Additional contact information
Leonid Serkin: Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior s/n, Coyoacán, Mexico City 04510, Mexico
Tatyana L. Belyaeva: Universidad Autónoma del Estado de México, Av. Instituto Literario 100, Toluca 50000, Mexico

Mathematics, 2025, vol. 13, issue 11, 1-28

Abstract: This review summarizes the application of physics-informed neural networks (PINNs) for solving higher-order nonlinear partial differential equations belonging to the nonlinear Schrödinger equation (NLSE) hierarchy, including models with external potentials. We analyze recent studies in which PINNs have been employed to solve NLSE-type evolution equations up to the fifth order, demonstrating their ability to obtain one- and two-soliton solutions, as well as other solitary waves with high accuracy. To provide benchmark solutions for training PINNs, we employ analytical methods such as the nonisospectral generalization of the AKNS scheme of the inverse scattering transform and the auto-Bäcklund transformation. Finally, we discuss recent advancements in PINN methodology, including improvements in network architecture and optimization techniques.

Keywords: PINN; NLSE; solitons; external potentials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/11/1882/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/11/1882/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:11:p:1882-:d:1671846

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().