Novel Soliton Solutions to KdV-Type Equations Based on Physics-Informed Neural Networks

QIU Tianwei; WEI Guangmei; SONG Yuxin; WANG Zhen

doi:10.21656/1000-0887.450122

Volume 46 Issue 1

Jan. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(1): 105-113

QIU Tianwei, WEI Guangmei, SONG Yuxin, WANG Zhen. Novel Soliton Solutions to KdV-Type Equations Based on Physics-Informed Neural Networks[J]. Applied Mathematics and Mechanics, 2025, 46(1): 105-113. doi: 10.21656/1000-0887.450122

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Novel Soliton Solutions to KdV-Type Equations Based on Physics-Informed Neural Networks

doi: 10.21656/1000-0887.450122

School of Mathematical Sciences, Beihang University, Beijing 100191, P.R.China

Received Date: 2024-04-30
Rev Recd Date: 2024-06-04
Publish Date: 2025-01-01

Abstract

Abstract

Physics-informed neural networks (PINNs) were applied in combination with generalized Miura transformations to investigate 3 KdV-type equations. Several novel soliton solutions, including the kink-bell solution of the mKdV equation, were derived analytically with the improved PINN method; a single-soliton-like solution of the KdV equation, was achieved through the Miura transformation; and a dark-soliton solution of a strongly nonlinear KdV equation, was obtained by means of both the generalized Miura transformation and the PINN methods. Comparison of the numerical results obtained under the PINN framework with the exact solutions from theoretical analysis shows that, the proposed algorithm effectively uncovers new numerical solutions of partial differential equations and offers valuable insights for theoretical research.
- physics-informed neural networks,
- Miura transformation,
- KdV-type equation,
- soliton,
- integrable system

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致谢: 本文作者衷心感谢北京航空航天大学敢为行动计划项目(JKF-20240582)对本文的资助.

References(19)

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