Symmetrical Lucas functions for the solutions of the lattice equation

In this paper, the auxiliary function method is proposed by studying the symmetrical Lucas sine function and symmetrical Lucas cosine function. This is the first time that the symmetrical Lucas functions are used to solve the solutions of the differential and difference equations. Then the method is applied to the lattice equation. Some new exact traveling wave solutions are obtained.

► In this paper, we study the auxiliary function method with the symmetrical Lucas sine function and symmetrical Lucas cosine function.
► This method gives the solutions of PDEs.
► This is the first time that the symmetrical Lucas functions are used to solve the solutions of PDEs.