Homotopy Analysis Solutions to Bubble Equations Through the Laplace Transform and Machine Learning

Qin Yupeng; Wang Shuo; Jin Hao; Wang Zhen; Zou Li

doi:10.21656/1000-0887.460144

Volume 47 Issue 9

Sep. 2026

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Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(9): 1211-1221

Qin Yupeng, Wang Shuo, Jin Hao, Wang Zhen, Zou Li. Homotopy Analysis Solutions to Bubble Equations Through the Laplace Transform and Machine Learning[J]. Applied Mathematics and Mechanics, 2026, 47(9): 1211-1221. doi: 10.21656/1000-0887.460144

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Homotopy Analysis Solutions to Bubble Equations Through the Laplace Transform and Machine Learning

doi: 10.21656/1000-0887.460144

Qin Yupeng^{1, 2
,},
Wang Shuo³,
Jin Hao³,
Wang Zhen⁴,
Zou Li^{5
,
,}

1.
School of Science, Henan Institute of Technology, Xinxiang, Henan 453003, P.R. China
2.
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, P.R. China
3.
School of Vehicle and Traffic Engineering, Henan Institute of Technology, Xinxiang, Henan 453003, P.R. China
4.
School of Mathematical Sciences, Beihang University, Beijing 100191, P.R. China
5.
School of Naval Architecture, Dalian University of Technology, Dalian, Liaoning 116024, P.R. China

Received Date: 2025-08-02
Rev Recd Date: 2025-11-12
Publish Date: 2026-09-01

Abstract

Abstract

The homotopy analysis method (HAM) is an important approach for solving nonlinear problems. The HAM was applied to construct high-precision approximate analytical solutions to the Rayleigh-Plesset equations for describing the periodic pulsation of bubbles in an ideal fluid. In the HAM framework, the Laplace transform was used to solve high-order deformation equations and obtain HAM solutions to the bubble equations. By means of the machine learning to optimize the convergence-control parameter in the HAM approximations, high-precision HAM approximations of the bubble equations were obtained. The results show that, the Laplace transform improves the efficiency of solving complex high-order deformation equations, and the machine learning technique provides an effective way to optimize the convergence control parameter in HAM approximations. Finally, as applications of the HAM approximations, dynamic characteristics and laws of bubble pulsation were discussed.
- bubble equation,
- Laplace transform,
- machine learning,
- homotopy analysis method,
- convergence-control parameter

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References(38)

References

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