IDEAS home Printed from https://ideas.repec.org/a/hin/complx/9314693.html
   My bibliography  Save this article

Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Author

Listed:
  • Yongyi Gu
  • Fanning Meng

Abstract

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the - expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al. , we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

Suggested Citation

  • Yongyi Gu & Fanning Meng, 2019. "Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods," Complexity, Hindawi, vol. 2019, pages 1-11, August.
    • Handle: RePEc:hin:complx:9314693
    DOI: 10.1155/2019/9314693
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/9314693.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/9314693.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/9314693?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
    ---><---

    References listed on IDEAS

    as
    1. Gao, Lijun & Wang, Dandan & Wang, Gang, 2015. "Further results on exponential stability for impulsive switched nonlinear time-delay systems with delayed impulse effects," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 186-200.
    2. Yuan, Wenjun & Meng, Fanning & Huang, Yong & Wu, Yonghong, 2015. "All traveling wave exact solutions of the variant Boussinesq equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 865-872.
    3. Shou-Ting Chen & Wen-Xiu Ma, 2019. "Exact Solutions to a Generalized Bogoyavlensky-Konopelchenko Equation via Maple Symbolic Computations," Complexity, Hindawi, vol. 2019, pages 1-6, January.
    4. Chaudry Masood Khalique, 2013. "On the Solutions and Conservation Laws of a Coupled Kadomtsev-Petviashvili Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, February.
    5. Zhang, Xinguang & Liu, Lishan & Wu, Yonghong & Wiwatanapataphee, B., 2015. "The spectral analysis for a singular fractional differential equation with a signed measure," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 252-263.
    6. Wen-Xiu Ma & Jie Li & Chaudry Masood Khalique, 2018. "A Study on Lump Solutions to a Generalized Hirota-Satsuma-Ito Equation in (2+1)-Dimensions," Complexity, Hindawi, vol. 2018, pages 1-7, December.
    7. Wang, Ying & Liu, Lishan & Zhang, Xinguang & Wu, Yonghong, 2015. "Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 312-324.
    Full references (including those not matched with items on IDEAS)

    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. Teng Ren & Helu Xiao & Zhongbao Zhou & Xinguang Zhang & Lining Xing & Zhongwei Wang & Yujun Cui, 2019. "The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process," Complexity, Hindawi, vol. 2019, pages 1-15, September.
    2. Fang Wang & Lishan Liu & Yonghong Wu & Yumei Zou, 2019. "Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p -Laplacian Operator," Complexity, Hindawi, vol. 2019, pages 1-21, October.
    3. Wu, Zhi-Jia & Tian, Shou-Fu, 2023. "Breather-to-soliton conversions and their mechanisms of the (2+1)-dimensional generalized Hirota–Satsuma–Ito equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 235-259.
    4. Longfei Lin & Yansheng Liu & Daliang Zhao, 2021. "Study on Implicit-Type Fractional Coupled System with Integral Boundary Conditions," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    5. Zhou, Boling & Yang, Yongqing & Xu, Xianyun, 2019. "The group-delay consensus for second-order multi-agent systems by piecewise adaptive pinning control in part of time interval," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 694-708.
    6. Wen-Xiu Ma, 2019. "Long-Time Asymptotics of a Three-Component Coupled mKdV System," Mathematics, MDPI, vol. 7(7), pages 1-38, June.
    7. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    8. Sheng Zhang & Yuanyuan Wei & Bo Xu, 2019. "Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example," Complexity, Hindawi, vol. 2019, pages 1-9, August.
    9. Bo Ren, 2019. "Dynamics Behavior of Lumps and Interaction Solutions of a (3+1)-Dimensional Partial Differential Equation," Complexity, Hindawi, vol. 2019, pages 1-8, April.
    10. Navickas, Z. & Ragulskis, M. & Telksnys, T., 2016. "Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 333-338.
    11. Wang, Yijing & Zou, Yanchao & Zuo, Zhiqiang & Li, Hongchao, 2016. "Finite-time stabilization of switched nonlinear systems with partial unstable modes," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 172-181.
    12. Li, Lili & Zhao, Dan & She, Mianfu & Chen, Xiaoli, 2022. "On high order numerical schemes for fractional differential equations by block-by-block approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    13. Youzheng Ding & Jiafa Xu & Zhengqing Fu, 2019. "Positive Solutions for a System of Fractional Integral Boundary Value Problems of Riemann–Liouville Type Involving Semipositone Nonlinearities," Mathematics, MDPI, vol. 7(10), pages 1-19, October.
    14. Shou-Ting Chen & Wen-Xiu Ma, 2019. "Exact Solutions to a Generalized Bogoyavlensky-Konopelchenko Equation via Maple Symbolic Computations," Complexity, Hindawi, vol. 2019, pages 1-6, January.
    15. Ju, Yanhao & Sun, Yuangong & Meng, Fanwei, 2020. "Stabilization of switched positive system with impulse and marginally stable subsystems: A mode-dependent dwell time method," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    16. Zhang, Jie & Sun, Yuangong, 2021. "Practical exponential stability of discrete-time switched linear positive systems with impulse and all modes unstable," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    17. Liu, Ling & Wen, Xiao-Yong & Liu, Nan & Jiang, Tao & Yuan, Jin-Yun, 2020. "An integrable lattice hierarchy associated with a 4 × 4 matrix spectral problem: N-fold Darboux transformation and dynamical properties," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    18. Oke Davies Adeyemo & Lijun Zhang & Chaudry Masood Khalique, 2022. "Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics," Mathematics, MDPI, vol. 10(14), pages 1-46, July.
    19. Wanassi, Om Kalthoum & Torres, Delfim F.M., 2023. "An integral boundary fractional model to the world population growth," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    20. Aziz Khan & Yongjin Li & Kamal Shah & Tahir Saeed Khan, 2017. "On Coupled -Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions," Complexity, Hindawi, vol. 2017, pages 1-9, August.

    More about this item

    Statistics

    Access and download statistics

    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:hin:complx:9314693. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.