Contents Preface xi Part 1. History, Basic Models, and Travelling Waves 1 Chapter 1. Introduction and a Brief Review of the History 3 Chapter 2. Basic Models 17 2.1. Introduction 17 2.2. Models 17 2.3. Comments 22 Chapter 3. Solitary and Periodic Travelling Wave Solutions 25 3.1. Introduction 25 3.2. Travelling Wave Solutions 25 3.3. Examples 27 3.4. The Poisson Summation Theorem and Periodic Wave Solutions 39 3.5. Comments 42 Part 2. Well-Posedness and Stability Definition 47 Chapter 4. Initial Value Problem 49 4.1. Introduction 49 4.2. Some Results about Well-Posedness 49 4.3. Some Results about Global Well-Posedness 57 4.4. Comments 58 Chapter 5. Definition of Stability 61 5.1. Introduction 61 5.2. Orbital Stability 61 5.3. Comments 64 Part 3. Stability Theory 67 Chapter 6. Orbital Stability—the Classical Method 69 6.1. Introduction 69 6.2. Stability of Solitary Wave Solutions for the GKdV 70 6.3. “Stability of the Blow-up” for a Class of KdV Equations 81 6.4. Comments 87 Chapter 7. Grillakis-Shatah-Strauss’s Stability Approach 91 7.1. Introduction 91 vii
Previous Page Next Page