معادلات غیرخطی پراکنده: وجود و پایداری راه‌حل‌های موجی تنها و دوره‌ای

"This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied includes Korteweg-de Vries, Benjamin-Ono, and Schrödinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena."--Publisher's website This Book Provides A Self-contained Presentation Of Classical And New Methods For Studying Wave Phenomena That Are Related To The Existence And Stability Of Solitary And Periodic Travelling Wave Solutions For Nonlinear Dispersive Evolution Equations. Simplicity, Concrete Examples, And Applications Are Emphasized Throughout In Order To Make The Material Easily Accessible. The List Of Classical Nonlinear Dispersive Equations Studied Includes Korteweg-de Vries, Benjamin-ono, And Schrödinger Equations. Many Special Jacobian Elliptic Functions Play A Role In These Examples. The Author Brings The Reader To The Forefront Of Knowledge About Some Aspects Of The Theory And Motivates Future Developments In This Fascinating And Rapidly Growing Field. The Book Can Be Used As An Instructive Study Guide As Well As A Reference By Students And Mature Scientists Interested In Nonlinear Wave Phenomena.--publisher's Website. Part 1: History, Basic Models, And Travelling Waves. Introduction And A Brief Review Of The History ; Basic Models ; Solitary And Periodic Travelling Wave Solutions. -- Part 2: Well-posedness And Stability Definition. Initial Value Problem ; Definition Of Stability. -- Part 3. Stability Theory. Orbital Stability--the Classical Method ; Grillakis-shatah-strauss's Stability Approach. -- Part 4. The Concentration-compactness Principle In Stability Theory. Existence And Stability Of Solitary Waves For The Gbo ; More About The Concentration-compactness Principle ; Instability Of Solitary Wave Solutions. -- Part 5. Stability Of Periodic Travelling Waves. Stability Of Cnoidal Waves. -- Part 6. Appendices. Jaime Angulo Pava. Includes Bibliographical References (p. 245-254) And Index.