• Continuous limit, higher-order rational solutions and relevant dynamical analysis for Belov–Chaltikian lattice equation with 3×3 Lax pair

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    • Keywords


      Belov–Chaltikian lattice equation; continuous limit; discrete generalised (m, 3Nm)-fold Darboux transformation; rational solution; singular trajectory analysis.

    • Abstract


      Belov–Chaltikian (BC) lattice equation, which is related to the research of lattice analogues of W-algebras, is under consideration in this work. This equation may be viewed as an extension of the Volterra lattice equation. Firstly, we correspond BC lattice equation to several continuous equations under the continuous limit. Secondly, based on the known 3 × 3 matrix form Lax pair of this discrete equation, we construct its discrete generalised (m, 3Nm)-fold Darboux transformation for the first time and successfully popularise this technique from 2×2 Lax pair to 3×3 Lax pair. Finally, by applying the resulting Darboux transformation, we get its higher order rational solutions and analyse their singular trajectories and dynamics using the graphics and limit-state analysis.

    • Author Affiliations



      1. School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, People’s Republic of China
    • Dates

  • Pramana – Journal of Physics | News

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