Dissipative solitons. From optics to biology and medicine
The collection of review articles aims to present the current states of theoretical research in the field of localized one- and two-dimensional patterns in models based on nonlinear partial differential equations of the Ginzburg-Landau type (sometimes these may be discrete equations or nonlocal ones). Equations of this type apply to the description of optical media (amplifiers, fiber lasers, cavities and others), nonlinear dissipative patterns in hydrodynamics (flows, cellular structures in thermal convection, etc.), and some examples from biology (in particular, vegetation patterns and neural networks). Some articles also include brief reviews of respective experimental results and phenomenological observations. Certain essential topics belonging to the area of dissipative solitons are not covered by the book. The articles of this volume will be reviewed individually. Indexed articles: \textit{Akhmediev, N.; Ankiewicz, A.}, Three sources and three component parts of the concept of dissipative solitons, 1-28 [Zbl 1218.35183] \textit{Velarde, M. G.; Nepomnyashchy, A. A.}, Solitons in viscous flows., 29-49 [Zbl 1218.76022] \textit{Lugiato, L. A.; Prati, F.; Tissoni, G.; Brambilla, M.; Barland, S.; Giudici, M.; Tredicce, J. R.}, Cavity solitons in semiconductor devices., 51-92 [Zbl 1218.82027] \textit{Rosanov, Nikolay N.; Fedorov, Sergey V.; Shatsev, Anatoly N.}, Dissipative solitons in laser systems with non-local and non-instantaneous nonlinearly, 93-111 [Zbl 1218.78123] \textit{Colet, P.; Gomila, D.; Jacobo, A.; Matías, M. A.}, Excitability mediated by dissipative solitons in nonlinear optical cavities, 113-135 [Zbl 1218.78105] \textit{Grelu, P.; Soto-Crespo, J. M.}, Temporal soliton ``molecules'' in mode-locked lasers: collisions, pulsations, and vibrations, 137-173 [Zbl 1218.78108] \textit{Mitschke, F.}, Compounds of fiber-optic solitons, 175-194 [Zbl 1218.78118] \textit{Turitsyn, S. K.; Boscolo, S.}, Dissipative nonlinear structures in fiber optics, 195-220 [Zbl 1218.78126] \textit{Montes, C.}, Three-wave dissipative Brillouin solitons, 221-260 [Zbl 1218.78119] \textit{Coulibaly, S.; Durniak, C.; Taki, Majid}, Spatial dissipative solitons under convective and absolute instabilities in optical parametric oscillators, 261-287 [Zbl 1218.78106] \textit{Flach, S.; Gorbach, Andrei V.}, Discrete breathers with dissipation, 289-320 [Zbl 1218.37107] \textit{Velarde, G.; Ebeling, Werner; Chetverikov, A. P.}, Anharmonic oscillations, dissipative solitons and non-Ohmic supersonic electric transport, 321-335 [Zbl 1218.78127] \textit{Gabitov, I. R.; Korotkevich, A. O.; Maimistov, A. I.; McMahon, J. B.}, Coherent optical pulse dynamics in nano-composite plasmonic Bragg gratings, 337-360 [Zbl 1218.82024] \textit{Saffman, M.; Wang, Yingxue}, Collective focusing and modulational instability of light and cold atoms, 361-380 [Zbl 1218.81118] \textit{Tlidi, M.; Lefever, R.; Vladimirov, A.}, On vegetation clustering, localized bare soil spots and fairy circles, 381-402 [Zbl 1218.92073] \textit{Golomb, D.}, Propagation of traveling pulses in cortical networks, 403-430 [Zbl 1218.92019] \textit{Troy, W. C.}, Wave phenomena in neuronal networks, 431-452 [Zbl 1218.92025] \textit{Zykov, V. S.}, Spiral waves and dissipative solitons in weakly excitable media, 453-473 [Zbl 1218.35201]
scientific article; zbMATH DE number 5299199