We analyze pulse propagation in a soliton fiber laser, modelled by the complex Schrödinger-Ginzburg-Landau equation. It is shown that this equation admits two previously unknown forms of stable stationary solutions. The first of them is a dual-frequency pulse, which propagates as a single unit, but has two symmetric peaks in the spectrum. The second one is a moving pulse, with the asymmetric double-hump spectrum.
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