A System of Nonlinear Differential-Difference Equations with Variable Coefficients and Its Reductions

摘要

Constructing integrable systems is a significant direction in soliton theory. In this paper, a new system of nonlinear differential-difference equations with variable coefficients is derived by introducing some derivable functions to the corresponding discrete spectral problems. In order to give some special cases of the derived differential-difference equations, three reductions are obtained which include Hirota's lattice equations as special cases. The processes of constructing such a system of variable-coefficient differential-difference equations and obtaining its reductions provide with a necessary help for the beginners.