The dissipative soliton concept is a fundamental extension of the concept of solitons in conservative and integrable systems. It includes ideas from three major sources, namely standard soliton theory developed since the 1960s, nonlinear dynamics theory and Prigogine's ideas of systems far from equilibrium. These three sources also correspond to theÊthree component parts of this novel paradigm. This book explains the above principles in detail and gives the reader various examples from optics, biology and medicine. These include laser systems, optical transmission lines, cortical networks, models of muscle contraction, localized vegetation structures and waves in brain tissues.

Contents

Three Sources and Three Component Parts of the Concept of Dissipative Solitons, N. Akhmediev and A. Ankiewicz

Solitons in Viscous Flows, Manuel G. Velarde and Alexander A. Nepomnyashchy

Cavity Solitons in Semiconductor Devices, L. A. Lugiato, F. Prati G. Tissoni, M. Brambilla, S. Barland, M. Giudici and J. Tredicce

Dissipative Solitons in Laser Systems with Non Local and Non Instantaneous Nonlinearity, Nikolay N. Rosanov, Sergey V. Fedorov and Anatoly N. Shatsev

Excitability Mediated by Dissipative Solitons in Nonlinear Optical Cavities, Pere Colet, Damia Gomila, Adrian Jacobo and Manuel A. Matias

Temporal Soliton Molecules in Mode Locked Lasers Collisions Pulsations and Vibrations, Philippe Grelu and Jose-Maria Soto-Crespo

Compounds of Fiber Optic Solitons, Fedor Mitschke

Dissipative Nonlinear Structures in Fiber Optics, Sergei K. Turitsyn and Sonia Boscolo

Three Wave Dissipative Brillouin Solitons, Carlos Montes

Spatial dissipative solitons under convective and absolute instabilities in optical parametric oscillators, Saliya Coulibaly, C eline Durniak and Majid Taki

Discrete Breathers with Dissipation, Sergej Flach and Andrey V. Gorbach

Anharmonic Oscillations, Dissipative Solitons and Non-Ohmic Supersonic Electric Transport, Manuel G. Velarde, Werner Ebeling and Alexander P. Chetverikov

Coherent Optical Pulse Dynamics in Nano composite Plasmonic Bragg Gratings, Ildar R. Gabitov, Alexander O. Korotkevich, Andrei I. Maimistov and Joseph B. McMahon

Collective focusing and modulational instability of light and cold atoms, Mark Saffman and Yingxue Wang

On Vegetation Clustering Localized Bare Soil Spots and Fairy Circles, Mustapha Tlidi, Rene Lefever and Andrei Vladimirov

Propagation of Traveling Pulses in Cortical Networks, David Golomb

Wave Phenomena in Neuronal Networks, William C. Troy

Spiral Waves and Dissipative Solitons inWeakly Excitable Media Vladimir S. Zykov

Sources