Description

Book Synopsis

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.



Trade Review

“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 Schrödinger 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 für Mathematik, Vol. 180, 2016)



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.

Introduction to Nonlinear Dispersive Equations Universitext

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    A Paperback by Felipe Linares, Gustavo Ponce

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      Book details

      Publisher Springer New York
      Published 12/15/2014 12:00:00 AM
      ISBN-13 9781493921805
      978-1493921805
      ISBN-10 1493921800
      Also in:
      Mathematics Differential calculus and equations

      Description

      Book Synopsis

      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.



      Trade Review

      “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 Schrödinger 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 für Mathematik, Vol. 180, 2016)



      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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