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An integrable lattice hierarchy associated with a 4 × 4 matrix spectral problem: N-fold Darboux transformation and dynamical properties

Author

Listed:
  • Liu, Ling
  • Wen, Xiao-Yong
  • Liu, Nan
  • Jiang, Tao
  • Yuan, Jin-Yun

Abstract

A new integrable hierarchy related to a 4 × 4 matrix isospectral problem is proposed, in which the semi-discrete version of the coupled KdV system is the first member. Subsequently the N-fold Darboux transformation for the second member in the obtained hierarchy is constructed. As applications, the explicitly exact solutions to the equation in three cases of different seed solutions are discussed and their graphs are showed to analyze the corresponding dynamical properties. Meanwhile some numerical simulations are given to illustrate these properties.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300319305041
    DOI: 10.1016/j.amc.2019.06.039
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    References listed on IDEAS

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    1. Hu, Bei-Bei & Xia, Tie-Cheng & Ma, Wen-Xiu, 2018. "Riemann–Hilbert approach for an initial-boundary value problem of the two-component modified Korteweg-de Vries equation on the half-line," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 148-159.
    2. 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.
    3. Kaup, D.J., 2005. "Variational solutions for the discrete nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(3), pages 322-333.
    4. Yu, Jianping & Jing, Jian & Sun, Yongli & Wu, Suping, 2016. "(n+1)-Dimensional reduced differential transform method for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 697-705.
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