Hardcover ISBN:  9781470436131 
Product Code:  GSM/182 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
Electronic ISBN:  9781470442286 
Product Code:  GSM/182.E 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 

Book DetailsGraduate Studies in MathematicsVolume: 182; 2017; 575 ppMSC: Primary 35; 37;
This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is exampleoriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs.
The book consists of four parts. Parts I and II are introductions to finite and infinitedimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Kortewegde Vries equation, the Nonlinear Schrödinger equation and the GinzburgLandau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given.
The parts of the book are kept as selfcontained as possible. The book is suitable for selfstudy, and there are various possibilities to build one or twosemester courses from the book.ReadershipGraduate students and researchers interested in nonlinear dynamics of PDEs.

Table of Contents

Chapters

Introduction

Basic ODE dynamics

Dissipative dynamics

Hamiltonian dynamics

PDEs on an interval

The NavierStokes equations

Some dissipative PDE models

Three canonical modular equations

Reactiondiffusion systems

Dynamics of pattern and the GL equation

Wave packets and the NLS equation

Long waves and their modular equations

Center manifold reduction and spatial dynamics

Diffusive stability


Additional Material

Reviews

This book as a whole is more than the sum of its chapters and deserves being slowly and thoughtfully read from the beginning to the end.
Michael Zaks, Mathematical Reviews 
This is an excellent text which can be used for several graduate courses in mathematics departments.
Dmitry Pelinovsky, Zentralblatt MATH 
The combination of rigor with simultaneous attention to associated real physical systems makes it particularly appealing.
William Satzer, MAA Reviews


RequestsReview Copy – for reviewers who would like to review an AMS bookDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is exampleoriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs.
The book consists of four parts. Parts I and II are introductions to finite and infinitedimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Kortewegde Vries equation, the Nonlinear Schrödinger equation and the GinzburgLandau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given.
The parts of the book are kept as selfcontained as possible. The book is suitable for selfstudy, and there are various possibilities to build one or twosemester courses from the book.
Graduate students and researchers interested in nonlinear dynamics of PDEs.

Chapters

Introduction

Basic ODE dynamics

Dissipative dynamics

Hamiltonian dynamics

PDEs on an interval

The NavierStokes equations

Some dissipative PDE models

Three canonical modular equations

Reactiondiffusion systems

Dynamics of pattern and the GL equation

Wave packets and the NLS equation

Long waves and their modular equations

Center manifold reduction and spatial dynamics

Diffusive stability

This book as a whole is more than the sum of its chapters and deserves being slowly and thoughtfully read from the beginning to the end.
Michael Zaks, Mathematical Reviews 
This is an excellent text which can be used for several graduate courses in mathematics departments.
Dmitry Pelinovsky, Zentralblatt MATH 
The combination of rigor with simultaneous attention to associated real physical systems makes it particularly appealing.
William Satzer, MAA Reviews