Chen, Liguo; Yang, Liangui; Zhang, Jiaqi; Wang, Jie Nonlinear Boussinesq equation with dissipation and topography forcing in stratified fluids and its solutions. (Chinese. English summary) Zbl 1463.76025 Math. Appl. 33, No. 2, 373-380 (2020). Summary: We investigate the dynamic model of nonlinear Rossby waves in stratified fluids. We derive a forced nonlinear Boussinesq equation to describe the amplitude evolution of nonlinear Rossby waves by considering the quasi-geostrophic baroclinic potential vorticity equation with dissipation and topography and external source, and by utilizing Gardner-Morikawa transform and the perturbation expansion method. The analytic and approximate solutions for the forced nonlinear Boussinesq equation are presented by the modified Jacobi elliptic function expansion method and the homotopy perturbation method. Result of solutions shows that the generalized \(\beta\), basic flow shear and stratification are extremely important factors inducing the nonlinear Rossby waves, dissipation and topography are external forcing factors affecting the evolution of nonlinear Rossby waves. MSC: 76D50 Stratification effects in viscous fluids 35Q53 KdV equations (Korteweg-de Vries equations) Keywords:Boussinesq equation; nonlinear Rossby wave; stratified fluids; dissipation; topography PDFBibTeX XMLCite \textit{L. Chen} et al., Math. Appl. 33, No. 2, 373--380 (2020; Zbl 1463.76025)