Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids
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...
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doaj-c24de0c5975f438b8d36a88db8b644602020-11-24T21:27:20ZengMDPI AGMathematics2227-73902019-01-01714110.3390/math7010041math7010041Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer FluidsLei Fu0Yaodeng Chen1Hongwei Yang2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaKey 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, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaIn 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.http://www.mdpi.com/2227-7390/7/1/41time-space fractional coupled generalized Zakharov-Kuznetsov equations setRossby wavesquasi-geostrophic vortex equationstwo-layer fluids |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lei Fu Yaodeng Chen Hongwei Yang |
spellingShingle |
Lei Fu Yaodeng Chen Hongwei Yang Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids Mathematics time-space fractional coupled generalized Zakharov-Kuznetsov equations set Rossby waves quasi-geostrophic vortex equations two-layer fluids |
author_facet |
Lei Fu Yaodeng Chen Hongwei Yang |
author_sort |
Lei Fu |
title |
Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids |
title_short |
Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids |
title_full |
Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids |
title_fullStr |
Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids |
title_full_unstemmed |
Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids |
title_sort |
time-space fractional coupled generalized zakharov-kuznetsov equations set for rossby solitary waves in two-layer fluids |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2019-01-01 |
description |
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. |
topic |
time-space fractional coupled generalized Zakharov-Kuznetsov equations set Rossby waves quasi-geostrophic vortex equations two-layer fluids |
url |
http://www.mdpi.com/2227-7390/7/1/41 |
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