Application of Fibonacci tane function to nonlinear differential-difference equations

The symmetrical Fibonacci tane is constructed according to the symmetrical Fibonacci sine and cosine [Stakhov A, Rozin B. Chaos, Solitons & Fractals 2005;23:379]. As one of its applications, an algorithm is devised to obtain exact traveling wave solutions for the differential-difference equations by means of the property of function tane. For illustration, we apply the method to the (2 + 1)-dimensional Toda lattice, the discrete nonlinear Schrödinger equation and a generalized Toda lattice, and successfully construct some explicit and exact traveling wave solutions.