Introduction to Nonlinear Dispersive Equations

• Main Authors: Ponce, Gustavo (Author), Linares, Felipe (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Universitext
• Subjects: Mathematics.; Partial differential equations.; Partial Differential Equations.

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 li...

Table of Contents:

• The Fourier Transform
• Interpolation of Operators. A Multiplier Theorem
• Sobolev Spaces and Pseudo-Differential Operators
• The Linear Schrodinger Equation
• The Nonlinear Schrodinger Equation. Local Theory
• Asymptotic Behavior for NLS Equation
• Korteweg-de Vries Equation
• Asymptotic Behavior for k-gKdV Equations
• Other Nonlinear Dispersive Models
• General Quasilinear Schrodinger Equation.