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Symmetry breaking and multi-hump solitons in inhomogeneous gain landscapes

We address one-dimensional soliton formation in the cubic nonlinear medium with two-photon absorption and transversally inhomogeneous gain landscape consisting of a single or several amplifying channels. Existence of the solitons requires certain threshold gain while the properties of solitons strongly depend on whether the number of the amplifying channels is odd or even. In the former case an increase of the gain leads to a symmetry breaking, which occurs through the pitchfork bifurcation, and to emergence of a single or several co-existing stable asymmetric modes. In the case of even number of amplifying channels we have found only asymmetric stable states.