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Introduction to Nonlinear Dispersive 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...

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Main Authors: Linares, Felipe. (Author, http://id.loc.gov/vocabulary/relators/aut), Ponce, Gustavo. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2015.
Edition:2nd ed. 2015.
Series:Universitext,
Subjects:
Partial differential equations.
Partial Differential Equations.
Online Access:https://doi.org/10.1007/978-1-4939-2181-2
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.

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