A New Variable-Coefficient Riccati Subequation Method for Solving Nonlinear Lattice Equations

and Applied Analysis 3 coth-function solution in [25, (41)] with a 1 = 0, a 2 = 1, Δ = −4σ, and −ε ln(−ε 0 )/2 = c 0 . φ 3 (ξ n ) is essentially equivalent to the tan-function solution in [25, (42)] with a 1 = 0, a 2 = 1, Δ = −4σ, and ξ 0 = c 0 , while φ 4 (ξ n ) is essentially equivalent to the cot-function solution in [25, (42)] with a 1 = 0, a 2 = 1, Δ = −4σ, and ξ 0 = c 0 . φ 7 (ξ n ) is essentially equivalent to the rational function solution in [25, (40)] with a 1 = 0, a 2 = 1, and ξ 0 = c 0 . Besides, our solution φ 5 (ξ n ) is not shown in [25]. 3. Application of the Variable-Coefficient Riccati Subequation Method to the Discrete (2 + 1)-Dimensional Toda Lattice Equation In this section, we will apply the described method in Section 2 to the discrete (2 + 1)-dimensional Toda lattice equation [13, 14]: