Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids

Lei Fu, Yaodeng Chen and Hongwei Yang
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Lei Fu: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Yaodeng Chen: Key Laboratory of Meteorological Disaster (KLME), Ministry of Education and Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science and Technology, Nanjing 210044, China
Hongwei Yang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2019, vol. 7, issue 1, 1-13

Abstract: In this paper, the theoretical model of Rossby waves in two-layer fluids is studied. A single quasi-geostrophic vortex equation is used to derive various models of Rossby waves in a one-layer fluid in previous research. In order to explore the propagation and interaction of Rossby waves in two-layer fluids, from the classical quasi-geodesic vortex equations, by employing the multi-scale analysis and turbulence method, we derived a new (2+1)-dimensional coupled equations set, namely the generalized Zakharov-Kuznetsov(gZK) equations set. The gZK equations set is an extension of a single ZK equation; they can describe two kinds of weakly nonlinear waves interaction by multiple coupling terms. Then, for the first time, based on the semi-inverse method and the variational method, a new fractional-order model which is the time-space fractional coupled gZK equations set is derived successfully, which is greatly different from the single fractional equation. Finally, group solutions of the time-space fractional coupled gZK equations set are obtained with the help of the improved ( G ′ / G ) -expansion method.

Keywords: time-space fractional coupled generalized Zakharov-Kuznetsov equations set; Rossby waves; quasi-geostrophic vortex equations; two-layer fluids (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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