IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v327y2018icp104-116.html
   My bibliography  Save this article

Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions

Author

Listed:
  • Lu, Changna
  • Fu, Chen
  • Yang, Hongwei

Abstract

Construct fractional order model to describe Rossby solitary waves can provide more pronounced effects and deeper insight for comprehending generalization and evolution of Rossby solitary waves in stratified fluid. In the paper, from the quasi-geostrophic vorticity equation with dissipation effect and complete Coriolis force, based on the multi-scale analysis and perturbation method, a classical generalized Boussinesq equation is derived to describe the Rossby solitary waves in stratified fluid. Further, by employing the reduction perturbation method, the semi-inverse method, the Agrawal method, we derive the Euler–lagrangian equation of classical generalized Boussinesq equation and obtain the time-fractional generalized Boussinesq equation. Without dissipation effect, by using Lie group analysis method, the conservation laws of time-fractional Boussinesq equation are given. Finally, with the help of the improved (G′/G) expansion method, the exact solutions of the above equation are generated. Meanwhile, in order to consider the dissipation effect, we have to derive the approximate solutions by adopting the New Iterative Method. We remark that the fractional order model can open up a new window for better understanding the waves in fluid.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:327:y:2018:i:c:p:104-116
    DOI: 10.1016/j.amc.2018.01.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318300316
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.01.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shuman Meng & Yujun Cui, 2019. "The Extremal Solution To Conformable Fractional Differential Equations Involving Integral Boundary Condition," Mathematics, MDPI, vol. 7(2), pages 1-9, February.
    2. Yin, Xiao-Jun & Yang, Lian-Gui & Liu, Quan-Sheng & Su, Jin-Mei & Wu, Guo-rong, 2018. "Structure of equatorial envelope Rossby solitary waves with complete Coriolis force and the external source," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 68-74.
    3. Lei Fu & Hongwei Yang, 2019. "An Application of (3+1)-Dimensional Time-Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves," Complexity, Hindawi, vol. 2019, pages 1-15, August.
    4. Rezapour, Sh. & Kumar, S. & Iqbal, M.Q. & Hussain, A. & Etemad, S., 2022. "On two abstract Caputo multi-term sequential fractional boundary value problems under the integral conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 365-382.
    5. Mouktonglang, Thanasak & Yimnet, Suriyon & Sukantamala, Nattakorn & Wongsaijai, Ben, 2022. "Dynamical behaviors of the solution to a periodic initial–boundary value problem of the generalized Rosenau-RLW-Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 114-136.
    6. 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.
    7. Haoyu Dong & Changna Lu & Hongwei Yang, 2018. "The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations," Mathematics, MDPI, vol. 6(10), pages 1-17, October.
    8. Rizvi, Syed Tahir Raza & Khan, Salah Ud-Din & Hassan, Mohsan & Fatima, Ishrat & Khan, Shahab Ud-Din, 2021. "Stable propagation of optical solitons for nonlinear Schrödinger equation with dispersion and self phase modulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 126-136.
    9. Min Guo & Chen Fu & Yong Zhang & Jianxin Liu & Hongwei Yang, 2018. "Study of Ion-Acoustic Solitary Waves in a Magnetized Plasma Using the Three-Dimensional Time-Space Fractional Schamel-KdV Equation," Complexity, Hindawi, vol. 2018, pages 1-17, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
    2. Tariq, Hira & Akram, Ghazala, 2017. "New approach for exact solutions of time fractional Cahn–Allen equation and time fractional Phi-4 equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 352-362.
    3. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:327:y:2018:i:c:p:104-116. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.