Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
1998-03-31
Nonlinear Sciences
Pattern Formation and Solitons
Latex, 96 pages, 39 postscript figures Manuscript restructured, some new results added
Scientific paper
We performed a comprehensive study of the spike autosolitons: self-sustained solitary inhomogeneous states, in the classical reaction-diffusion system --- the Gray-Scott model. We developed singular perturbation techniques based on the strong separation of the length scales to construct asymptotically the solutions in the form of a one-dimensional static autosolitons, higher-dimensional radially-symmetric static autosolitons, and two types of traveling autosolitons. We studied the stability of the static autosolitons in one and three dimensions and analyzed the properties of the static and the traveling autosolitons.
Muratov Cyrill B.
Osipov Vasiliy
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