This textbook introduces the well-posedness theory for initial-value problems of nonlinear
dispersive partial differential equations with special focus on two key models the
Korteweg-de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained
treatment of background material (the Fourier transform interpolation theory Sobolev spaces
and the linear Schrödinger equation) prepares the reader to understand the main topics covered:
the initial-value problem for the nonlinear Schrödinger equation and the generalized
Korteweg-de Vries equation properties of their solutions and a survey of general classes of
nonlinear dispersive equations of physical and mathematical significance. Each chapter ends
with an expert account of recent developments and open problems as well as exercises. The
final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger
equation taking the reader to the forefront of recent research. The second edition of
Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by
the addition of updated material on the main topics an expanded bibliography and new
exercises. Assuming only basic knowledge of complex analysis and integration theory this book
will enable graduate students and researchers to enter this actively developing field.
