Mixed rational-soliton solutions of two differential-difference equations in Casorati determinant form

By reconsidering soliton solutions of the Toda lattice and differential-difference KdV equation in the Casorati determinant form with new entries, we obtain rational and mixed rational-soliton solutions in the Casorati determinant form. All these solutions are verified by direct substitutions into bilinear equations. The method used is general and can apply to other discrete systems.