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Revisit to self-organization of solitons for dissipative Korteweg-de Vries equation
Author(s) -
Yasumitsu Kondoh,
J. W. Van Dam
Publication year - 1995
Language(s) - English
Resource type - Reports
DOI - 10.2172/86289
Subject(s) - dissipative system , korteweg–de vries equation , dissipation , dissipative operator , self organization , nonlinear system , operator (biology) , physics , dissipative soliton , classical mechanics , mathematical physics , soliton , computer science , quantum mechanics , chemistry , biochemistry , repressor , artificial intelligence , transcription factor , gene
The process by which self-organization occurs for solitons described by the Korteweg-de Vries (KdV) equation with a viscous dissipation term is reinvestigated theoretically, with the use of numerical simulations in a periodic system. It is shown that, during nonlinear interactions, two basic processes for the self-organization of solitons are energy transfer and selective dissipation among the eigenmodes of the dissipative operator. It is also clarified that an important process during nonlinear self-organization is an interchange between the dominant operators, which has hitherto been overlooked in conventional self-organization theories and which leads to a final self-similar coherent structure determined uniquely by the dissipative operator

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