A Differential-Difference Hierarchy Related to the Toda Lattice and Its Inverse Scattering Transformation
Received:November 13, 2020  Revised:January 28, 2021
Key Word: Toda lattice   inverse scattering transformation   soliton solution  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11671177; 11771186) and Postgraduate Research $\&$ Practice Innovation Program of Jiangsu Province (Grant No.KYCX21_2566).
Author NameAffiliation
Zexuan ZHANG School of Mathematics and Statistics, Jiangsu Normal University, Jiangsu 221116, P. R. China 
Jianbing ZHANG School of Mathematics and Statistics, Jiangsu Normal University, Jiangsu 221116, P. R. China 
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Abstract:
      By combined power evolution laws of the spectral parameter λ and the initial constants of integration, a new differential-difference hierarchy is presented from the Toda spectral problem. The hierarchy contains the classic Toda lattice equation, the nonisospectral Toda lattice equation and the mixed Toda lattice equation as reduced cases. The evolution of the scattering data in the inverse scattering transform is analyzed in detail and exact soliton solutions are computed through the corresponding inverse scattering transform.
Citation:
DOI:10.3770/j.issn:2095-2651.2022.01.006
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