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Explicit Solutions and Conservation Laws for a New Integrable Lattice Hierarchy

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  • 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
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    References listed on IDEAS

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    1. Fan Zhang, 2019. "In the Dark," World Bank Publications - Books, The World Bank Group, number 30923.
    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. 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.
    4. 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.
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