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A discrete generalization of the extended simplest equation method. (English) Zbl 1222.65114

Summary: We modify the so-called extended simplest equation method to obtain discrete traveling wave solutions for nonlinear differential-difference equations. The Wadati lattice equation is chosen to illustrate the method in detail. Further discrete soliton/periodic solutions with more arbitrary parameters, as well as discrete rational solutions, are revealed. We note that using our approach one can also find in principal highly accurate exact discrete solutions for other lattice equations arising in the applied sciences.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35C07 Traveling wave solutions
34A33 Ordinary lattice differential equations
37K60 Lattice dynamics; integrable lattice equations
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