Colloquium Publications 1999; 182 pp; hardcover Volume: 46 ISBN10: 0821819194 ISBN13: 9780821819197 List Price: US$44 Member Price: US$35.20 Order Code: COLL/46
 This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrödinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented. Several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs. Readership Graduate students and research mathematicians interested in PDEs and related areas. Table of Contents  Introduction and summary
 An overview of results on the Cauchy problem for NLS
 Further comments
 3D \(H^1\)critical defocusing NLS
 Global wellposedness below energy norm
 Nonlinear Schrödinger equation with periodic boundary conditions
 Growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
 Zakharov systems
 References
 Index
