New Nonlinear Difference-Differential Equation Related to the Volterra Equation

We propose a new type of nonlinear difference-differential equations. We find its transformation relation to the discrete KdV equation, and based on it find an N-soliton solution. We find expressions of 1- and 2-soliton solutions and discuss their properties. We find an elliptic function solution, and derive from it a 1-soliton solution under a nonvanishing boundary condition at the infinity.