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Darboux transformations and discrete soliton dynamics in a general Toda-type lattice system

Author

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  • Shen, Yuan
  • Wu, Xi-Hu
  • Zhang, Rui-Jie
  • Zhao, Xin
  • Cheng, Chong-Dong
  • Zhou, Tian-Yu

Abstract

This work studies a general Toda-type lattice system that contains the Toda lattice, the relativistic Toda lattice, and other related integrable systems as special cases. The primary innovation of this work lies in the construction of a 2N-fold Darboux transformation through an appropriate Darboux matrix combined with a gauge transformation, where N is a positive integer. On this basis, we further propose a novel generalized (m,2N−m)-fold Darboux transformation involving m distinct spectral parameters, with m being a positive integer. By employing these two Darboux transformations, we derive a variety of analytical solutions, including the discrete soliton solutions, rational solutions, and mixed solutions. These results reveal the rich solution structure of lattice systems and provide theoretical insights into the nonlinear phenomena in discrete integrable systems.

Suggested Citation

  • Shen, Yuan & Wu, Xi-Hu & Zhang, Rui-Jie & Zhao, Xin & Cheng, Chong-Dong & Zhou, Tian-Yu, 2026. "Darboux transformations and discrete soliton dynamics in a general Toda-type lattice system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 781-793.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:781-793
    DOI: 10.1016/j.matcom.2026.04.037
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    References listed on IDEAS

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    1. Ma, Wen-Xiu & Maruno, Ken-ichi, 2004. "Complexiton solutions of the Toda lattice equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 219-237.
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