Integrability and Darboux Transformation of a Four-component Volterra Lattice Equation

A four-component Volterra (fc-Volterra) lattice hierarchy is proposed from a 4 x 4 matrix spectral problem. Through the continuous limit, the first member of the fc-Volterra lattice hierarchy yields the generalized coupled KdV equation, which has important physical applications. We construct the Darboux transformation (DT) and exact solutions for the fcperiodic interaction solution, and rational-exponential interaction solution. Furthermore, we present the continuous limit for the linear spectral problem and soliton solutions of the fc-Volterra lattice equation, considering spatial step tends to zero.