Higher-Order Solitons Of The Discrete Ragnisco-Tu Equation

The discrete Ragnisco-Tu equation is an important model of discrete integrable system, and the study about the Ragnisco-Tu equation is meaningful. On use of the spectral analysis about the discrete spectral problem of the Ragnisco-Tu equation, a nonregular Riemann-Hilbert problem with non-normalization condition is constructed, and the relationship between the Ragnisco-Tu potential and the solution of the Riemann-Hilbert problem is established. The nonregular Riemann-Hilbert problems with the simple zeros and higher-order zeros are discussed respectively. The representation of the solution of the Ragnisco-Tu equation about the soliton matrix is obtained, and the higher-order soliton solutions and the simple soliton solutions are given.