In addition to pedagogical and new material, each chapter reviews the current state of the area and discusses classic and open problems in engaging, surprisingly non-technical ways. The contributors are Brian Davies (bifurcations in maps), Nalini Joshi (integrable systems and asymptotics), Alan Newell (wave turbulence and pattern formation), Mark Ablowitz (nonlinear waves), Carl Weiss (spatial solitons), Cathy Holmes (Hamiltonian systems), Tony Roberts (dissipative fluid mechanics), Jorgen Frederiksen (two-dimensional turbulence), and Mike Lieberman (Fermi acceleration).

Contents:

• Nonlinearity and Complexity: An Introduction (B Davies)
• Hunting Mathematical Butterflies (N Joshi)
• The Dynamics of Fermi Acceleration: From Cosmic Rays to Discharge Heating (M A Lieberman)
• Large Resonances in Hamiltonian Systems, with Applications (C Holmes)
• Structure Functions, Cumulants and Breakdown Criteria for Wave Turbulence (L J Biven et al.)
• Renormalized Closure Theory and Subgrid-Scale Parametrizations for Two-Dimensional Turbulence (J S Frederiksen)
• Low-Dimensional Modelling of Dynamical Systems Applied to Some Dissipative Fluid Mechanics (A J Roberts)
• Vortices and Spatial Solitons in Optical Resonators, and the Relations to Other Fields of Physics (C O Weiss et al.)
• Nonlinear Waves and (Interesting) Applications (M J Ablowitz et al.)
• Global Description of Patterns Far from Onset: A Case Study (N Ercolani et al.)