Wang, Danni; Yang, Hongli; Yang, Liangui Derivation of a higher order nonlinear Schrödinger equation with complete Coriolis force. (Chinese. English summary) Zbl 1438.35400 Acta Math. Sci., Ser. A, Chin. Ed. 38, No. 5, 883-892 (2018). Summary: In this paper, based on the barotropic potential vorticity equation with complete Coriolis force, a new higher order nonlinear Schrödinger equation is derived by using perturbation expansion method to describe nonlinear modulated Rossby waves in the geophysical fluid. From this equation, the modulational wave trains are discussed. It is found that the horizontal component term of Coriolis force and the topography term have an effect on the uniform Rossby wave trains and the instability region has changed. In addition, the uniform background basic flow does affect the modulational instability of solitary Rossby wave train. MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 76B47 Vortex flows for incompressible inviscid fluids Keywords:complete Coriolis force; Rossby waves; higher order nonlinear Schrödinger equation; modulational disturbances PDFBibTeX XMLCite \textit{D. Wang} et al., Acta Math. Sci., Ser. A, Chin. Ed. 38, No. 5, 883--892 (2018; Zbl 1438.35400)