Solitary wave and periodic wave solutions for the quintic discrete nonlinear Schrödinger equation

In this paper, we construct a new truncation function expansion approach to investigate exact solutions for the quintic discrete nonlinear Schrödinger equation. As a result, many types of exact solutions are obtained which includes discrete bell-type solitary wave solution, solitary wave solution, triangular periodic wave solution, alternating phase bell-type solitary wave solution, alternating phase solitary wave solution, and alternating phase triangular periodic wave solution. The properties of some new exact solutions are shown in figures.