TY - CHAP
T1 - Three sources and three component parts of the concept of dissipative solitons
AU - Akhmediev, N.
AU - Ankiewicz, A.
PY - 2008
Y1 - 2008
N2 - We explain the notion of dissipative solitons within a historical perspective. We show that the ideas of the theory of dissipative solitons emerge from several fields, including classical soliton theory, nonlinear dynamics, with its theory of bifurcations, and Prigogine's concept of self-organization. A new notion, emerging from this three-part foundation, allows us to build the novel concept of the dissipative soliton. We also show that reductions to lower dimensional systems have to be done carefully and should always include a comparison of the results with numerical simulations of the original equations.
AB - We explain the notion of dissipative solitons within a historical perspective. We show that the ideas of the theory of dissipative solitons emerge from several fields, including classical soliton theory, nonlinear dynamics, with its theory of bifurcations, and Prigogine's concept of self-organization. A new notion, emerging from this three-part foundation, allows us to build the novel concept of the dissipative soliton. We also show that reductions to lower dimensional systems have to be done carefully and should always include a comparison of the results with numerical simulations of the original equations.
UR - http://www.scopus.com/inward/record.url?scp=57749169730&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-78217-9_1
DO - 10.1007/978-3-540-78217-9_1
M3 - Chapter
SN - 9783540782162
T3 - Lecture Notes in Physics
SP - 1
EP - 28
BT - Dissipative Solitons
A2 - Akhmediev, Nail
A2 - Ankiewicz, Adrian
ER -