The Nonlinear Schroedinger Equations Self-Focusing and Wave Collapse

Catherine Sulem , Pierre-Louis Sulem

Table of contents :
Header……Page 1
Cover……Page 4
Preface……Page 6
Contents……Page 12
Part I – Basic Framework……Page 18
1 – The Physical Context……Page 20
2 – Structural Properties……Page 44
Part II – Rigorous Theory……Page 58
3 – Existence and Long-Time Behavior……Page 60
4 – Standing Wave Solutions……Page 88
5 – Blowup Solutions……Page 110
Part III – Asymptotic Analysis near Collapse……Page 130
6 – Numerical Observations……Page 132
7 – Supercritical Collapse……Page 150
8 – Critical Collapse……Page 158
9 – Perturbations of Focusing NLS……Page 178
Part IV – Coupling to a Mean Field……Page 204
10 – Mean Field Gravitation……Page 206
11 – Gravity-Capillary Surface Waves……Page 222
12 – The Davey-Stewartson System……Page 238
Part V – Coupling to Acoustic Waves……Page 260
13 – Langmuir Oscillations……Page 262
14 – The Scalar Model……Page 280
15 – Progressive Waves in Plasmas……Page 304
Synopsis……Page 324
References……Page 326