The Nonlinear Schrödinger Equation

Self-Focusing and Wave Collapse

Catherine Sulem, Pierre-Louis Sulem (Autoren)

Buch | Hardcover

350 Seiten

1999 | 1999 ed.
Springer-Verlag New York Inc.
9780387986111 (ISBN)

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Filling the gap between the mathematical literature and applications to domains, this title addresses 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.

Reihe/Serie	Applied Mathematical Sciences ; 139
Zusatzinfo	XVI, 350 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
	Technik ► Maschinenbau
ISBN-13	9780387986111 / 9780387986111
Zustand	Neuware