Static spike autosolitons in the Gray-Scott model

C. B. Muratov; V. V. Osipov

doi:10.1088/0305-4470/33/48/321

Static spike autosolitons in the Gray-Scott model

C. B. Muratov
, V. V. Osipov

Research output: Contribution to journal › Article › peer-review

70 Scopus citations

Abstract

We construct asymptotically the solutions to a classical reaction-diffusion system (the Gray-Scott model of an autocatalytic reaction) in the form of static spike autosolitons (self-sustained solitary pulses, spots and clots). We show that solutions in the form of static spike autosolitons exist over a wide range of system parameters in one dimension, and in a narrower range of parameters in two and three dimensions. We study the properties of these solutions.

Original language	English (US)
Pages (from-to)	8893-8916
Number of pages	24
Journal	Journal of Physics A: Mathematical and General
Volume	33
Issue number	48
DOIs	https://doi.org/10.1088/0305-4470/33/48/321
State	Published - Dec 8 2000

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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10.1088/0305-4470/33/48/321

Cite this

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title = "Static spike autosolitons in the Gray-Scott model",

abstract = "We construct asymptotically the solutions to a classical reaction-diffusion system (the Gray-Scott model of an autocatalytic reaction) in the form of static spike autosolitons (self-sustained solitary pulses, spots and clots). We show that solutions in the form of static spike autosolitons exist over a wide range of system parameters in one dimension, and in a narrower range of parameters in two and three dimensions. We study the properties of these solutions.",

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AU - Osipov, V. V.

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N2 - We construct asymptotically the solutions to a classical reaction-diffusion system (the Gray-Scott model of an autocatalytic reaction) in the form of static spike autosolitons (self-sustained solitary pulses, spots and clots). We show that solutions in the form of static spike autosolitons exist over a wide range of system parameters in one dimension, and in a narrower range of parameters in two and three dimensions. We study the properties of these solutions.

AB - We construct asymptotically the solutions to a classical reaction-diffusion system (the Gray-Scott model of an autocatalytic reaction) in the form of static spike autosolitons (self-sustained solitary pulses, spots and clots). We show that solutions in the form of static spike autosolitons exist over a wide range of system parameters in one dimension, and in a narrower range of parameters in two and three dimensions. We study the properties of these solutions.

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U2 - 10.1088/0305-4470/33/48/321

DO - 10.1088/0305-4470/33/48/321

M3 - Article

AN - SCOPUS:0034623753

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 48

ER -

Static spike autosolitons in the Gray-Scott model

Abstract

All Science Journal Classification (ASJC) codes

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