Introduction to Nonlinear Dispersive Equations

This text is designed for graduate students. It covers the basics of the field before moving to advanced material and offers key tools in harmonic and Fourier analysis. Each chapter concludes with recent developments, open problems and exercises.

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The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way. The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces. The authors then proceed to use the linear Schrodinger equation to describe properties enjoyed by general dispersive equations. This information is then used to treat local and global well-posedness for the semi-linear Schrodinger equations. The end of each chapter contains recent developments and open problems, as well as exercises.