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The Nonlinear Schroedinger Equation - Singular Solutions and Optical Collapse (Hardcover)
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The Nonlinear Schroedinger Equation - Singular Solutions and Optical Collapse (Hardcover)
Series: Applied Mathematical Sciences, 192
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This book is an interdisciplinary introduction to optical collapse
of laser beams, which is modelled by singular (blow-up) solutions
of the nonlinear Schroedinger 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 Schroedinger
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. Gadi
Fibich is a Professor of Applied Mathematics at Tel Aviv
University. "This book provides a clear presentation of the
nonlinear Schrodinger equation and its applications from various
perspectives (rigorous analysis, informal analysis, and physics).
It will be extremely useful for students and researchers who enter
this field." Frank Merle, Universite de Cergy-Pontoise and Institut
des Hautes Etudes Scientifiques, France
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