This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (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.
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 Schrodinger equation with periodic boundary conditions Growth of Sobolev norms in linear Schrodinger equations with smooth time dependent potential Zakharov systems References Index.