The Nonlinear Schrödinger Equation
Self-Focusing and Wave Collapse
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ISBN-13:
9781475773071
Veröffentl:
2013
Einband:
Paperback
Erscheinungsdatum:
14.03.2013
Seiten:
372
Autor:
Pierre-Louis Sulem
Gewicht:
563 g
Format:
235x155x21 mm
Serie:
139, Applied Mathematical Sciences
Sprache:
Englisch
Beschreibung:
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.
This monograph reviews in detail significant results concerning the phenomena of wave collapse, as described by the NLS equation, or its generalization when couplings to additional fields driven by the wave modulation are relevant. Several approaches, ranging from rigorous mathematical analysis to formal asymptotics expansions and numerical simulations are presented.
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.
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