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

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 β effects, respectively.