Felipe Linares is a Researcher at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil. Gustavo Ponce is a Professor of Mathematics at the University of California in Santa Barbara.

"This is the second edition of a self-contained graduate level introduction to the results and methods in the well-posedness theory for initial-value problems of nonlinear dispersive equations with special focus on the nonlinear Schrodinger and Korteweg de Vries equations. ... I strongly welcome this updated version and I can only recommend it warmly to anybody (both students and teachers) interested in this central area of analysis." (G. Teschl, Monatshefte fur Mathematik, Vol. 180, 2016)

• 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.

Felipe Linares is a Researcher at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil. Gustavo Ponce is a Professor of Mathematics at the University of California in Santa Barbara.

"This is the second edition of a self-contained graduate level introduction to the results and methods in the well-posedness theory for initial-value problems of nonlinear dispersive equations with special focus on the nonlinear Schrodinger and Korteweg de Vries equations. ... I strongly welcome this updated version and I can only recommend it warmly to anybody (both students and teachers) interested in this central area of analysis." (G. Teschl, Monatshefte fur Mathematik, Vol. 180, 2016)

• 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.

Felipe Linares is a Researcher at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil. Gustavo Ponce is a Professor of Mathematics at the University of California in Santa Barbara.

"This is the second edition of a self-contained graduate level introduction to the results and methods in the well-posedness theory for initial-value problems of nonlinear dispersive equations with special focus on the nonlinear Schrodinger and Korteweg de Vries equations. ... I strongly welcome this updated version and I can only recommend it warmly to anybody (both students and teachers) interested in this central area of analysis." (G. Teschl, Monatshefte fur Mathematik, Vol. 180, 2016)

• 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.