Introduction to Nonlinear Dispersive Equations

• Main Authors: Linares, Felipe (Author), Ponce, Gustavo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2015.
• Edition: 2nd ed. 2015.
• Series: Universitext,
• Subjects: Mathematics.; Partial differential equations.; Partial Differential Equations.

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 mat...

Table of Contents:

• 1. The Fourier Transform
• 2. Interpolation of Operators
• 3. Sobolev Spaces and Pseudo-Differential Operators
• 4. The Linear Schrodinger Equation
• 5. The Non-Linear Schrodinger Equation
• 6. Asymptotic Behavior for NLS Equation
• 7. Korteweg-de Vries Equation
• 8. Asymptotic Behavior for k-gKdV Equations
• 9. Other Nonlinear Dispersive Models
• 10. General Quasilinear Schrodinger Equation
• Proof of Theorem 2.8
• Proof of Lemma 4.2
• References
• Index.