Abstract
The onset of patterns due to a localized gain is studied analytically in the framework of a real or complex amplitude equation. The instability modes are found, and the bifurcation of small localized solutions is analyzed. Some exact solutions are also found.
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Nepomnyashchy, A.A. (2013). Pattern Formation Under a Localized Gain. In: Malomed, B. (eds) Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Progress in Optical Science and Photonics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10091_2012_26
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DOI: https://doi.org/10.1007/10091_2012_26
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