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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.

Differential equations, Partial. --- Nonlinear wave equations. --- Nonlinear wave equations --- Differential equations, Partial --- Engineering & Applied Sciences --- Applied Mathematics --- Partial differential equations --- Mathematics. --- Partial differential equations. --- Partial Differential Equations. --- Math --- Science --- Wave equation --- Differential equations, partial.