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

Author

Listed:
  • 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
    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)

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.

Suggested Citation

  • Lei Fu & Yaodeng Chen & Hongwei Yang, 2019. "Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:41-:d:194715
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    References listed on IDEAS

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    1. Zeidan, D., 2016. "Assessment of mixture two-phase flow equations for volcanic flows using Godunov-type methods," Applied Mathematics and Computation, Elsevier, vol. 272(P3), pages 707-719.
    2. Minhajul, & Zeidan, D. & Raja Sekhar, T., 2018. "On the wave interactions in the drift-flux equations of two-phase flows," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 117-131.
    3. Abdon Atangana & Aydin Secer, 2013. "The Time-Fractional Coupled-Korteweg-de-Vries Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, March.
    4. Hongwei Yang & Qingfeng Zhao & Baoshu Yin & Huanhe Dong, 2013. "A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    5. Mengshuang Tao & Huanhe Dong, 2017. "Algebro-Geometric Solutions for a Discrete Integrable Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-9, November.
    6. Hongwei Yang & Baoshu Yin & Yunlong Shi & Qingbiao Wang, 2012. "Forced ILW-Burgers Equation as a Model for Rossby Solitary Waves Generated by Topography in Finite Depth Fluids," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, October.
    7. Eslami, Mostafa, 2016. "Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 141-148.
    8. Lu, Changna & Fu, Chen & Yang, Hongwei, 2018. "Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 104-116.
    9. Sahoo, S. & Saha Ray, S., 2016. "Solitary wave solutions for time fractional third order modified KdV equation using two reliable techniques (G′/G)-expansion method and improved (G′/G)-expansion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 265-282.
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