Thulasidharan, K and Vishnu Priya, N and Monisha, S and Senthilvelan, M (2024) Predicting positon solutions of a family of nonlinear Schrödinger equations through deep learning algorithm. In: Physics Letters, Section A: General, Atomic and Solid State Physics, 511 .
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Abstract
We consider a hierarchy of nonlinear Schrödinger equations (NLSEs) and forecast the evolution of positon solutions using a deep learning approach called Physics Informed Neural Networks (PINN). Notably, the PINN algorithm accurately predicts positon solutions not only in the standard NLSE but also in other higher order versions, including cubic, quartic and quintic NLSEs. The PINN approach also effectively handles two coupled NLSEs and two coupled Hirota equations. In addition to the above, we report exact second-order positon solutions of the sextic NLSE and coupled generalized NLSE. These solutions are not available in the existing literature and we construct them through generalized Darboux transformation method. Further, we utilize PINNs to forecast their behaviour as well. To validate PINN's accuracy, we compare the predicted solutions with exact solutions obtained from analytical methods. The results show high fidelity and low mean squared error in the predictions generated by our PINN model. © 2024 Elsevier B.V.
| Item Type: | Journal Article |
|---|---|
| Publication: | Physics Letters, Section A: General, Atomic and Solid State Physics |
| Publisher: | Elsevier B.V. |
| Additional Information: | The copyright for this article belongs to author. |
| Keywords: | Deep learning; Forecasting; Mean square error; Nonlinear equations, Deep learning; High-order; Higher-order; Hirota equation; Learning approach; Neural networks algorithms; Neural-networks; Nonlinear schrödinge equation; Positons; Quintic, Learning algorithms |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 29 May 2024 05:39 |
| Last Modified: | 29 May 2024 05:39 |
| URI: | https://eprints.iisc.ac.in/id/eprint/85004 |
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