1. Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions
- Author
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Bao Jun Zhao, Ru Yun Wang, Wen Jin Sun, and Hong Wei Yang
- Subjects
combined ZK-mZK equation ,Rossby solitary waves ,complete Coriolis force ,semi-inverse variational principle ,conservation laws ,Mathematics ,QA1-939 - Abstract
Abstract In the present paper, a new partial differential equation has been obtained to describe the Rossby solitary waves with complete Coriolis force by employing multi-scale analysis and perturbation method, we call it combined ZK-mZK equation. The equation can reflect the propagation of Rossby waves on the plane and is more appropriate for the real ocean and atmosphere than the ( 1 + 1 ) $(1+1)$ dimensional models (such as KdV and mKdV), which can only represent the propagation of Rossby solitary waves in a line. Furthermore, by adopting the multiplier method, we construct conservation laws of the combined ZK-mZK equation, which is meaningful for researching the global stability of solutions. Finally, we deduce the exact solutions of the combined ZK-mZK equation via the semi-inverse variational principle. By applying these exact solutions, some propagation features of Rossby solitary waves are analyzed.
- Published
- 2018
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