Soliton dynamics based on exact solutions of conformable fractional discrete complex cubic Ginzburg–Landau equation

Abstract

The Jacobian elliptic function expansion method is modified by considering conformable fractional derivative and applying a lot of relations among Jacobian elliptic functions. This modified method is applied to derive the discrete fractional soliton solutions of conformable fractional discrete complex cubic Ginzburg–Landau equation, including Jacobian elliptic function solutions and some special soliton and triangular function solutions. The singularity like tan and sec solutions ‘between sites’ can be avoided in the lattice. Based on these analytical solutions, the influence of the linear dissipation and filter parameters on wave amplitude modulations and optical explosive excitations is studied.