TY - JOUR
T1 - Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions
T2 - A review and a perspective
AU - Cartes, C.
AU - Descalzi, O.
AU - Brand, H. R.
N1 - Publisher Copyright:
© 2014, EDP Sciences and Springer.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - We review the work on exploding dissipative solitons in one and two spatial dimensions. Features covered include: the transition from modulated to exploding dissipative solitons, the analogue of the Ruelle-Takens scenario for dissipative solitons, inducing exploding dissipative solitons by noise, two classes of exploding dissipative solitons in two spatial dimensions, diffusing asymmetric exploding dissipative solitons as a model for a two-dimensional extended chaotic system. As a perspective we outline the interaction of exploding dissipative solitons with quasi one-dimensional dissipative solitons, breathing quasi one-dimensional solutions and their possible connection with experimental results on convection, and the occurence of exploding dissipative solitons in reaction-diffusion systems.It is a great pleasure to dedicate this work to our long-time friend Hans (Prof. Dr. Hans Jürgen Herrmann) on the occasion of his 60th birthday.
AB - We review the work on exploding dissipative solitons in one and two spatial dimensions. Features covered include: the transition from modulated to exploding dissipative solitons, the analogue of the Ruelle-Takens scenario for dissipative solitons, inducing exploding dissipative solitons by noise, two classes of exploding dissipative solitons in two spatial dimensions, diffusing asymmetric exploding dissipative solitons as a model for a two-dimensional extended chaotic system. As a perspective we outline the interaction of exploding dissipative solitons with quasi one-dimensional dissipative solitons, breathing quasi one-dimensional solutions and their possible connection with experimental results on convection, and the occurence of exploding dissipative solitons in reaction-diffusion systems.It is a great pleasure to dedicate this work to our long-time friend Hans (Prof. Dr. Hans Jürgen Herrmann) on the occasion of his 60th birthday.
UR - http://www.scopus.com/inward/record.url?scp=84920842590&partnerID=8YFLogxK
U2 - 10.1140/epjst/e2014-02255-2
DO - 10.1140/epjst/e2014-02255-2
M3 - Review article
AN - SCOPUS:84920842590
SN - 1951-6355
VL - 223
SP - 2145
EP - 2159
JO - European Physical Journal: Special Topics
JF - European Physical Journal: Special Topics
IS - 11
ER -