Asymmetric dissipative solitons in a waveguide lattice with non-uniform gain-loss distributions

We address the existence and stability of two types of asymmetric dissipative solitons, including fundamental and dipole solitons, supported by a waveguide lattice with non-uniform gain-loss distributions. Fundamental solitons exist only when the linear gain width is greater than or equal to the linear loss width, while dipole solitons exist only when the linear gain width is less than or equal to the linear loss width. With an increase in the relative gain depth, the effective width of the soliton gradually decreases. In addition, we find that both asymmetric fundamental and dipole solitons are stable in a considerable part of their lower edge of existence regions, and solitons beyond this range are unstable.