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We study discrete solitons in zigzag discrete waveguide arrays with differenttypes of linear mixing between nearest-neighbor and next-nearest-neighborcouplings. The waveguide array is constructed from two layers ofone-dimensional (1D) waveguide arrays arranged in zigzag form. If wealternately label the number of waveguides between the two layers, thecross-layer couplings (which couple one waveguide in one layer with twoadjacent waveguides in the other layer) construct the nearestneighborcouplings, while the couplings that couple this waveguide with the twonearest-neighbor waveguides in the same layer, i.e., self-layer couplings,contribute the next-nearest-neighbor couplings. Two families of discretesolitons are found when these couplings feature different types of linearmixing. As the total power is increased, a phase transition of the second kindoccurs for discrete solitons in one type of setting, which is formed when thenearest-neighbor coupling and next-nearest-neighbor coupling feature positiveand negative linear mixing, respectively. The mobilities and collisions ofthese two families of solitons are discussed systematically throughout thepaper, revealing that the width of the soliton plays an important role in its

Discrete solitons in zigzag waveguide arrays with different types of linear mixing between nearest-neighbor and next-nearest-neighbor couplings