IDEAS home Printed from https://ideas.repec.org/a/hin/complx/5984356.html

Explicit Solutions and Conservation Laws for a New Integrable Lattice Hierarchy

Author

Listed:
  • Qianqian Yang
  • Qiulan Zhao
  • Xinyue Li

Abstract

An integrable lattice hierarchy is derived on the basis of a new matrix spectral problem. Then, some properties of this hierarchy are shown, such as the Liouville integrability, the bi-Hamiltonian structure, and infinitely many conservation laws. After that, the Darboux transformation of the first integrable lattice equation in this hierarchy is constructed. Eventually, the explicitly exact solutions of the integrable lattice equation are investigated via graphs.

Suggested Citation

  • Qianqian Yang & Qiulan Zhao & Xinyue Li, 2019. "Explicit Solutions and Conservation Laws for a New Integrable Lattice Hierarchy," Complexity, Hindawi, vol. 2019, pages 1-10, June.
    • Handle: RePEc:hin:complx:5984356
    DOI: 10.1155/2019/5984356
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/5984356.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/5984356.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/5984356?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. Chen, Su-Su & Tian, Bo & Liu, Lei & Yuan, Yu-Qiang & Zhang, Chen-Rong, 2019. "Conservation laws, binary Darboux transformations and solitons for a higher-order nonlinear Schrödinger system," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 337-346.
    2. McAnally, Morgan & Ma, Wen-Xiu, 2018. "An integrable generalization of the D-Kaup–Newell soliton hierarchy and its bi-Hamiltonian reduced hierarchy," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 220-227.
    3. repec:wbk:wbpubs:30923 is not listed on IDEAS
    4. Ma, W.X., 1995. "Symmetry constraint of MKdV equations by binary nonlinearization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 467-481.
    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. Xianghua Jiang & Xifang Cao, 2022. "Darboux transformation and novel solitons of a coupled system," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(2), pages 413-424, June.
    2. 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.
    3. Wen-Xiu Ma, 2019. "Long-Time Asymptotics of a Three-Component Coupled mKdV System," Mathematics, MDPI, vol. 7(7), pages 1-38, June.
    4. Shi, Yu-Ren & Yang, Xue-Ying & Tang, Na & Wang, Deng-Shan, 2018. "Effects of Zeeman field on the dynamical instability of flat states for spin-2 Bose–Einstein condensates in an optical lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 39-55.
    5. Pengbo Wan & Jalil Manafian & Hajar Farhan Ismael & Sizar Abid Mohammed, 2020. "Investigating One‐, Two‐, and Triple‐Wave Solutions via Multiple Exp‐Function Method Arising in Engineering Sciences," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    6. Tongshuai Liu & Huanhe Dong, 2019. "The Prolongation Structure of the Modified Nonlinear Schrödinger Equation and Its Initial-Boundary Value Problem on the Half Line via the Riemann-Hilbert Approach," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    7. Ma, Yu-Lan & Li, Bang-Qing, 2022. "Kraenkel-Manna-Merle saturated ferromagnetic system: Darboux transformation and loop-like soliton excitations," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

    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:5984356. 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.