Discrete solitons in competitive zigzag waveguide arrays with cubic-quintic nonlinearity

In this paper, we study one-dimensional discrete solitons in zigzag waveguide arrays with competitive cubic-quintic nonlinearity and competitive linear mixing between the nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings. The competitive nonlinearity features a cubic self-focusing associated with a quintic self-defocusing nonlinearities. The competitive linear mixing between the NN and NNN couplings is induced by making the two coefficients opposite of each other, which is assumed to be induced by the embedding synthetic gauge phase within the coupling constants. The combination of these two types of competition, linear mixing and nonlinearity can create four types of soliton: multipeak bell-shaped solitons, multipeak flat-top solitons, staggered bell-shaped solitons, and staggered flat-top solitons. The stability and dynamics of these types of solitons are verified systematically through the paper. The total power and the types of competition between the linear mixing play important roles in tuning these solitons.