The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse

by Catherine Sulem, Pierre-Louis Sulem

Overview

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

ISBN-13:	9781475773071
Publisher:	Springer New York
Publication date:	03/14/2013
Series:	Applied Mathematical Sciences , #139
Edition description:	Softcover reprint of the original 1st ed. 1999
Pages:	350
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table 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.