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An integrable generalization of the D-Kaup–Newell soliton hierarchy and its bi-Hamiltonian reduced hierarchy

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  • McAnally, Morgan
  • Ma, Wen-Xiu

Abstract

We present a new spectral problem, a generalization of the D-Kaup–Newell spectral problem, associated with the Lie algebra sl(2,R). Zero curvature equations furnish the soliton hierarchy. The trace identity produces the Hamiltonian structure for the hierarchy and shows its Liouville integrability. Lastly, a reduction of the spectral problem is shown to have a different soliton hierarchy with a bi-Hamiltonian structure. The major motivation of this paper is to present spectral problems that generate two soliton hierarchies with infinitely many conservation laws and high-order symmetries.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:323:y:2018:i:c:p:220-227
    DOI: 10.1016/j.amc.2017.11.004
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

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