A differential-difference hierarchy related to the Toda lattice and its inverse scattering transformation
Received:November 13, 2020  Revised:January 12, 2021
Key Word: Toda lattice   inverse scattering transformation   soliton solution  
Fund ProjectL:The National Natural Science Foundation of China (No.11101350,11771186, 11671177).
Author NameAffiliationAddress
Jian-bing ZHANG School of Mathematics and Statistics , Jiangsu Normal University The Address of Quanshan Campus: No.101, Shanghai Road, Tongshan District, Xuzhou, Jiangsu Province P.R.China
Ze-xuan ZHANG School of Mathematics and Statistics , Jiangsu Normal University The Address of Quanshan Campus: No.101, Shanghai Road, Tongshan District, Xuzhou, Jiangsu Province 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.
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