Abstract
We consider the simplest mathematical model of localized dissipative structures described by a single diffusive equation with the source containing both local and global nonlinearities, i.e., depending on an integral of the unknown function over the entire volume. On the basis of qualitative analysis, we find out that stable autosolitons exist in the medium considered. This conclusion is confirmed by the results of numerical simulation of a three-dimensional problem. We determine the dependence of the autosoliton power on the parameters of the problem. Metastable multisoliton states are found and their properties are studied. The possibility of stabilization of three-dimensional autosolitons in a system without local losses is considered.
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Sonnemann, G., Semenov, V.E. Autosolitons in systems with global nonlinearity. Radiophysics and Quantum Electronics 44, 368–374 (2001). https://doi.org/10.1023/A:1017941028919
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DOI: https://doi.org/10.1023/A:1017941028919