On the topographic Rossby solitary waves via physical-informed neural networks

doi:10.1088/1674-1056/adc7f1

中国物理B ›› 2025, Vol. 34 ›› Issue (7): 70504-070504.doi: 10.1088/1674-1056/adc7f1

On the topographic Rossby solitary waves via physical-informed neural networks

Wenxu Liu(刘文绪), Ligeyan Dao(道力格艳), and Ruigang Zhang(张瑞岗)†

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

收稿日期:2025-02-02 修回日期:2025-03-26 接受日期:2025-04-02 出版日期:2025-06-18 发布日期:2025-06-30
通讯作者: Ruigang Zhang E-mail:rgzhang@imu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12462021, 12102205, and 12262025), the Central Guidance for Local Scientific and Technological Development Funding Projects (Grant No. 2024ZY0117), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No. NJYT23098), the Scientific Starting and the Innovative Research Team in the Universities of Inner Mongolia Autonomous Region of China (Grant No. NMGIRT2208), and the National College Students Innovation and Entrepreneurship Training Program (Grant No. 202410126024).

On the topographic Rossby solitary waves via physical-informed neural networks

Wenxu Liu(刘文绪), Ligeyan Dao(道力格艳), and Ruigang Zhang(张瑞岗)†

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received:2025-02-02 Revised:2025-03-26 Accepted:2025-04-02 Online:2025-06-18 Published:2025-06-30
Contact: Ruigang Zhang E-mail:rgzhang@imu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12462021, 12102205, and 12262025), the Central Guidance for Local Scientific and Technological Development Funding Projects (Grant No. 2024ZY0117), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No. NJYT23098), the Scientific Starting and the Innovative Research Team in the Universities of Inner Mongolia Autonomous Region of China (Grant No. NMGIRT2208), and the National College Students Innovation and Entrepreneurship Training Program (Grant No. 202410126024).

摘要/Abstract

摘要： In the generation and propagation of nonlinear Rossby solitary waves within the atmosphere and ocean, topography occupies a pivotal role. This paper focuses on elucidating the impact of topography on such Rossby solitary waves. Utilizing the perturbation expansion method and spatialtemporal transformations, we derive the Korteweg-de Vries and modified Korteweg-de Vries equation (Gardner equation) governing the amplitude of nonlinear Rossby waves. A fundamental issue addressed herein is a Sturm-Liouville-type ordinary differential equation characterized by variable coefficients and fixed boundary conditions. To numerically solve the derived Korteweg-de Vries and modified Korteweg-de Vries equations, we employ a physical-informed neural network. Both qualitative and quantitative analyses are conducted to discuss the influences of topography and $\beta$ effects, respectively.

关键词: Rossby solitary wave, shallow water models, topography, physical-informed neural network

Abstract: In the generation and propagation of nonlinear Rossby solitary waves within the atmosphere and ocean, topography occupies a pivotal role. This paper focuses on elucidating the impact of topography on such Rossby solitary waves. Utilizing the perturbation expansion method and spatialtemporal transformations, we derive the Korteweg-de Vries and modified Korteweg-de Vries equation (Gardner equation) governing the amplitude of nonlinear Rossby waves. A fundamental issue addressed herein is a Sturm-Liouville-type ordinary differential equation characterized by variable coefficients and fixed boundary conditions. To numerically solve the derived Korteweg-de Vries and modified Korteweg-de Vries equations, we employ a physical-informed neural network. Both qualitative and quantitative analyses are conducted to discuss the influences of topography and $\beta$ effects, respectively.

Key words: Rossby solitary wave, shallow water models, topography, physical-informed neural network

中图分类号: (Solitons)

05.45.Yv

02.30.Mv (Approximations and expansions) 47.11.St (Multi-scale methods) 92.10.hf (Planetary waves, Rossby waves)

Wenxu Liu(刘文绪), Ligeyan Dao(道力格艳), and Ruigang Zhang(张瑞岗). On the topographic Rossby solitary waves via physical-informed neural networks[J]. 中国物理B, 2025, 34(7): 70504-070504.

Wenxu Liu(刘文绪), Ligeyan Dao(道力格艳), and Ruigang Zhang(张瑞岗). On the topographic Rossby solitary waves via physical-informed neural networks[J]. Chin. Phys. B, 2025, 34(7): 70504-070504.

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On the topographic Rossby solitary waves via physical-informed neural networks

On the topographic Rossby solitary waves via physical-informed neural networks

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