Fibich G. The Nonlinear Schrödinger Equation. Singular Solutions and Optical Collapse

Springer International Publishing Switzerland, 2015 — 862 pp. — (Applied Mathematical Sciences 192). — ISBN: 978-3-319-12747-7 (Print) 978-3-319-12748-4 (Online).This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results.The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics.Provides a unique interdisciplinary treatment of the nonlinear Schrödinger equation, combining rigorous analysis, informal analysis, numerical methods and physics
Presents all the necessary physical background, and assumes only that the reader has taken an introductory class in partial differential equations
Carefully explains the theory, application and background of the nonlinear Schrödinger equation in nonlinear optics
Covers the theory of NLS collapse from the early 1960s and up to the present