Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Nonlinear Dispersive Equations: Existence and Stability of Solitary and Periodic Travelling Wave Solutions
 
Jaime Angulo Pava IME-USP, São Paulo, Brazil
Nonlinear Dispersive Equations
Hardcover ISBN:  978-0-8218-4897-5
Product Code:  SURV/156
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1383-5
Product Code:  SURV/156.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4897-5
eBook: ISBN:  978-1-4704-1383-5
Product Code:  SURV/156.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Nonlinear Dispersive Equations
Click above image for expanded view
Nonlinear Dispersive Equations: Existence and Stability of Solitary and Periodic Travelling Wave Solutions
Jaime Angulo Pava IME-USP, São Paulo, Brazil
Hardcover ISBN:  978-0-8218-4897-5
Product Code:  SURV/156
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1383-5
Product Code:  SURV/156.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4897-5
eBook ISBN:  978-1-4704-1383-5
Product Code:  SURV/156.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1562009; 256 pp
    MSC: Primary 76; 35; 37; 45; Secondary 34; 47;

    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.

    Readership

    Graduate students and research mathematicians interested in nonlinear wave phenomena.

  • Table of Contents
     
     
    • History, basic models, and travelling waves
    • 1. Introduction and a brief review of the history
    • 2. Basic models
    • 3. Solitary and periodic travelling wave solutions
    • Well-posedness and stability definition
    • 4. Introduction to part 2: well-posedness and stability definition
    • 5. Initial value problem
    • 6. Definition of stability
    • Stability theory
    • 7. Introduction to part 3: stability theory
    • 8. Orbital stability—the classical method
    • 9. Grillakis-Shatah-Strauss’s stability approach
    • The Concentration-Compactness Principle in stability theory
    • 10. Introduction to part 4: the concentration-compactness principle in the stability theory
    • 11. Existence and stability of solitary waves for the GBO equations
    • 12. More about the Concentration-Compactness Principle
    • 13. Instability of solitary wave solutions
    • Stability of periodic travelling waves
    • 14. Introduction to part 5: stability of periodic travelling waves
    • 15. Stability of cnoidal waves
    • Appendices
    • 16. Introduction to part 6: appendix
    • 17. Sobolev spaces and elliptic functions
    • 18. Operator theory
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1562009; 256 pp
MSC: Primary 76; 35; 37; 45; Secondary 34; 47;

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.

Readership

Graduate students and research mathematicians interested in nonlinear wave phenomena.

  • History, basic models, and travelling waves
  • 1. Introduction and a brief review of the history
  • 2. Basic models
  • 3. Solitary and periodic travelling wave solutions
  • Well-posedness and stability definition
  • 4. Introduction to part 2: well-posedness and stability definition
  • 5. Initial value problem
  • 6. Definition of stability
  • Stability theory
  • 7. Introduction to part 3: stability theory
  • 8. Orbital stability—the classical method
  • 9. Grillakis-Shatah-Strauss’s stability approach
  • The Concentration-Compactness Principle in stability theory
  • 10. Introduction to part 4: the concentration-compactness principle in the stability theory
  • 11. Existence and stability of solitary waves for the GBO equations
  • 12. More about the Concentration-Compactness Principle
  • 13. Instability of solitary wave solutions
  • Stability of periodic travelling waves
  • 14. Introduction to part 5: stability of periodic travelling waves
  • 15. Stability of cnoidal waves
  • Appendices
  • 16. Introduction to part 6: appendix
  • 17. Sobolev spaces and elliptic functions
  • 18. Operator theory
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.