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 solitar...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 andβeffects,respectively.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12462021,12102205,12262025)the Central Guidance for Local Scientific and Technological Development Funding Projects(Grant No.2024ZY0117)+2 种基金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)the National College Students Innovation and Entrepreneurship Training Program(Grant No.202410126024)。
文摘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 andβeffects,respectively.
