Topographic Algebraic Rossby Solitary Waves: A Study Using Physics-Informed Neural Networks

This study explores the influence of topography on Rossby solitary waves by analyzing the dynamics in both inner and outer regions, with solutions matched at the boundary. Using perturbation methods, the Benjamin–Davis–Ono (BDO) equation is derived from the shallow-water equations to characterize the amplitude evolution of Rossby algebraic solitary waves. The Physics-Informed Neural Networks (PINNs) method is applied to numerically solve the BDO equation, effectively capturing its nonlinear behavior and simulating the propagation of Rossby algebraic solitary waves under diverse topographic and external conditions. The results demonstrate that variations in key parameters significantly alter topographic effects, thereby impacting the amplitude of solitary waves. These findings provide valuable insights into the potential consequences of global warming and other external disturbances on the behavior of Rossby waves.