Emerging Frontiers in Nonlinear Science

This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal feature in mathematics, physics, chemistry and biology, and is used to characterize systems whose behavior does not amount to a superposition of simple building blocks, but rather features complex and often chaotic patterns and phenomena. Each chapter of the book features a synopsis that not only recaps the recent progress in each field but also charts the challenges that lie ahead.   

Chapter 1 – Nonlinearity and Biology (Zoi Rapti).- Chapter 2 - Nonlinearity and Topology (Avadh Saxena, Panayotis G. Kevrekidis, and Jesús Cuevas-Maraver).- Chapter 3 - Nonlinear Metamaterials (Lei Xu, Mohsen Rahmani, David A. Powell, Dragomir Neshev, Andrey E. Miroshnichenko).- Chapter 4 - Nonlinearity and discreteness: solitons in lattices (Boris A. Malomed).- Chapter 5 - Universal relaxation in quantum systems (Kazuya Fujimoto and Masahito Ueda).- Chapter 6 - Nonlinearity and Networks: A 2020 Vision (Mason A. Porter).- Chapter 7 - Integrability and Nonlinear Waves (Mark J. Ablowitz).- Chapter 8 - Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport (Stefano Iubini, Stefano Lepri, Roberto Livi, Antonio Politi, and Paolo Politi).- Chapter 9 - Nonlinearity, Geometry and Field Theory Solitons (Nicholas S. Manton).- Chapter 10 - Nonlinear and Novel Phenomena in Non-Hermitian Photonics (Li Ge and Wenjie Wan).- Chapter 11 - Computational Challenges of Nonlinear Systems (Laurette S. Tuckerman).- Chapter 12 - Dissipative Systems (Edgar Knobloch).- Chapter 13 - Synchronization in discrete models (Alexandre Rosas, Daniel Escaff, Katja Lindenberg).- Chapter 14 – Physics-informed learning machines for partial differential equations: Gaussian processes versus neural network (Guofei Pang and George Em Karniadakis).-Chapter 15- Nonlinear systems for unconventional computing (Kirill P. Kalinin and Natalia G. Berloff).