Linear superposition principle for partially coherent solitons

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Abstract
The existence of a linear superposition principle is demonstrated for partially coherent solitons with identical intensity profiles that are supported by the same medium. Since such degenerate partially coherent solitons are generic for saturable as well as for Kerr-like nonlinear media, our results are relevant to any noninstantaneous nonlinear media. The proposed superposition principle suggests a physical interpretation of partially coherent solitons as generalized linear modes of their self-induced waveguides. The power of such a superposition principle is illustrated by identifying soliton structures with controllable coherence properties both in logarithmically saturable and in Kerr-like nonlinear media.