The periodic wave solutions of the Wadati lattice equation

An extended expanding approach based on the work presented by Zhang is introduced for which some elliptic and hyperbolic function solutions to the Wadati lattice equation are obtained, which implement the resulting results given by Zhang. The way discovered in the paper can apply in other differential-difference equations for deducing exact soliton solutions.

Research highlights
► Introduced new formal solution (3) and (4).
► Presented another solution (5) and (6).
► New periodic wave solutions of the Wadati lattice equations were obtained.