Zhao, Bo; Yang, Liangui; Song, Jian Rossby waves under the influence of the vertical shear of basic flow beta effect forcing dissipation and topographic effect in the rotational stratified fluid. (Chinese. English summary) Zbl 1389.76011 Math. Appl. 30, No. 2, 424-433 (2017). Summary: In this paper, based on perturbation method and WKB method as well as the quasigeostrophic potential vorticity equation, we analyze the influence of the vertical shear of basic flow and stratification effect on Rossby waves including forcing dissipation and beta effect and topographic effect in the rotational stratified atmosphere. As a consequence, we obtain a nonlinear nonstandard Schrödinger equation. There is an envelope solitary wave solution when the wave number of Rossby envelope solitary waves is less than 3. Thus, we obtain that the vertical shear of basic flow has an influence on the wave velocity of Rossby envelope solitary waves and that the forcing dissipation on the stability of Rossby envelope solitary waves. We also obtain the longitude structure of Rossby envelope solitary waves from nonhomogeneous Bessel equation by using constant variation method. MSC: 76B65 Rossby waves (MSC2010) 76E30 Nonlinear effects in hydrodynamic stability Keywords:nonlinear Schrödinger equation; Rossby envelope solitary wave; vertical shear of basic flow; stratification effect PDFBibTeX XMLCite \textit{B. Zhao} et al., Math. Appl. 30, No. 2, 424--433 (2017; Zbl 1389.76011)