Wigner measure and semiclassical limits of nonlinear Schrödinger equations / Ping Zhang

Author(s): Zhang, Ping, 1969-
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Subjects: Schrödinger equation
WKB approximation
Differential equations, Nonlinear
Nonlinear theories
Formats: Print
Material Type: Books
Language: English
Audience: Unspecified
Published: Providence, R.I. : American Mathematical Society ; New York, N.Y. : Courant Institute of Mathematical Sciences, c2008
Series: Courant lecture notes in mathematics 17
LC Classification: Q, QC
Physical Description: viii, 197 p. ; 26 cm
Table of Contents: Ch. 1. The Classical WKB Method 1
Ch. 2. Wigner Measure 11
Ch. 3. The Limit from the One-Dimensional Schrodinger-Poisson to Vlasov-Poisson Equations 37
Ch. 4. Semiclassical Limit of Schrodinger-Poisson Equations 81
Ch. 5. Semiclassical Limit of the Cubic Schrodinger Equation in an Exterior Domain 105
Ch. 6. Incompressible and Compressible Limits of Coupled Systems of Nonlinear Schrodinger Equations 129
Ch. 7. High-Frequency Limit of the Helmholtz Equation 153
App. A. Global Solutions to (3.14) 173
App. B. Denseness of Polynomials 177
App. C. Global Existence of a Solution to (5.1) 179
App. D. Global Smooth Solution to (6.1) 189
Bibliography 193
Notes: LCCN: 2008028025
ISBN: 9780821847015 (alk. paper)
ISBN: 0821847015 (alk. paper)
Includes bibliographical references (p. 193-197)
OCLC Number: 233173132
ISBN/ISSN: 9780821847015