Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics. The text covers a wide spectrum of current research on the subject, which is an extremely active field in physics and mathematical physics, with a very broad range of implications, both for fundamental science and technological applications: light propagation in microstructured optical fibers, Bose-Einstein condensates, disordered systems, and the newly emerging field of nonlinear quantum mechanics.

Accessible to PhD students, this book will also be of interest to post-doctoral researchers and seasoned academics.

Inhalt

Sergej Flach: Nonlinear LatticeWaves in Random Potentials.- Xavier Antoine and Romain Duboscq: Modeling and computation of Bose-Einstein condensates: stationary states, nucleation, dynamics, stochasticity.- Stephan De Bièvre, François Genoud and Simona Rota Nodari: Orbital stability: analysis meets geometry.- Fabricio Macià: High-frequency dynamics for the Schrödinger equation, with applications to dispersion and observability.