The Nonlinear Schrödinger Equation - Self-Focusing and Wave Collapse

Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

List of contents

Basic Framework.- The Physical Context.- Structural Properties.- Rigorous Theory.- Existence and Long-Time Behavior.- Standing Wave Solutions.- Blowup Solutions.- Asymptotic Analysis near Collapse.- Numerical Observations.- Supercritical Collapse.- Critical Collapse.- Perturbations of Focusing NLS.- Coupling to a Mean Field.- Mean Field Generation.- Gravity-Capillary Surface Waves.- The Davey-Stewartson System.- Coupling to Acoustic Waves.- Langmuir Oscillations.- The Scalar Model.- Progressive Waves in Plasmas.

Summary

Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

Product details

• Authors: Catherin Sulem, Catherine Sulem, Pierre-Louis Sulem
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 17.10.2013
• EAN: 9781475773071
• ISBN: 978-1-4757-7307-1
• No. of pages: 350
• Dimensions: 155 mm x 22 mm x 237 mm
• Weight: 584 g
• Illustrations: XVI, 350 p.
• Series: Applied Mathematical Sciences; Applied Mathematical Sciences
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis