The process by which self-organization occurs for solitons described by the Korteweg–de Vries 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.

• Received 15 March 1995

DOI:https://doi.org/10.1103/PhysRevE.52.1721