Dissipative Solitons

N. Akhmediev, A. Ankiewicz (auth.), Nail Akhmediev, Adrian Ankiewicz (eds.)3540233733, 9783540233732

This volume is devoted to the exciting topic of dissipative solitons, i.e. pulses or spatially localised waves in systems exhibiting gain and loss. Examples are laser systems, nonlinear resonators and optical transmission lines. The physical principles and mathematical concepts are explained in a clear and concise way, suitable for students and young researchers. The similarities and differences in the notion of a soliton between dissipative systems and Hamiltonian and integrable systems are discussed, and many examples are given. The contributions are written by the world’s leading experts in the field, making it a unique exposition of this emerging topic.

Table of contents :
Dissipative Solitons in the Complex Ginzburg-Landau and Swift-Hohenberg Equations….Pages 1-17
Dissipative Magneto-Optic Solitons….Pages 19-35
Dissipative Solitons in Semiconductor Optical Amplifiers….Pages 37-54
Dissipative Solitons in Pattern-Forming Nonlinear Optical Systems: Cavity Solitons and Feedback Solitons….Pages 55-100
Solitons in Laser Systems with Saturable Absorption….Pages 101-130
Spatial Resonator Solitons….Pages 131-160
Dynamics of Dissipative Temporal Solitons….Pages 161-181
Soliton Dynamics in Mode-Locked Lasers….Pages 183-206
Temporal Multi-Soliton Complexes Generated by Passively Mode-Locked Lasers….Pages 207-239
Mode-Locking of Fiber Lasers via Nonlinear Mode-Coupling….Pages 241-265
Dissipative Solitons in Reaction-Diffusion Systems….Pages 267-308
Discrete Ginzburg-Landau Solitons….Pages 309-325
Discrete Dissipative Solitons….Pages 327-341
Nonlinear Schrödinger Equation with Dissipation: Two Models for Bose-Einstein Condensates….Pages 343-371
Solitary Waves of Nonlinear Nonintegrable Equations….Pages 373-406
Stability Analysis of Pulses via the Evans Function: Dissipative Systems….Pages 407-428
Bifurcations and Strongly Amplitude-Modulated Pulses of the Complex Ginzburg-Landau Equation….Pages 429-443